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### Interpreting Data - Relationship Between Weight and Height

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Interpreting Data - Relationship Between Weight and Height

MayfieldSchoolis a secondary school of 1183 pupils aged 11-16 years of
age. For my data handling coursework I have got to investigate a line
of enquiry from the pupils' data. Some of the options include;
relationship between IQ and Key Stage 3 results, comparing hair colour
and eye colour, but I have chosen to investigate the relationship
between height and weight. One of the main reasons being that this
line of enquiry means that my data will be numerical, allowing me to
produce a more detailed analysis rather than eye or hair colour where
I would be quite limited as to what I can do.

If I were to make an original prediction of my results, my hypothesis
would be;

"The taller the pupil, the heavier they will weigh."

In this project I will consider the link between height and weight and
will eventually be able to state whether my original hypothesis is in
fact correct. Other factors I am going to consider when performing
this investigation, is the effect of age and gender in my results and
I will make further hypothesize when I reach that stage in my project.

Collecting Data

I have originally decided to take a random sample of 30 girls and 30
boys; this will leave me with a total of 60 pupils. I have chosen to
use this amount as I feel this will be an adequate amount to retrieve
results and conclusions from, although on the other hand it is not too
many which would make my graph work far more difficult and in some
cases harder to work with. To retrieve my data I am going to firstly
use a random sample as this means that my data is not biased in any
way, and all of the pupils will vary in height, weight and age -
although I will have an equal gender ratio. To obtain this sample, I
could have written the numbers of all 580 girls in one hat, and 603
boys in the other, then selected 30 bits of paper from either hat and
look up their details from the number they are in the register.
Although I though an easier way of performing this task is by using
the 'Rand' button on my calculator. To retrieve 30 random numbers I
would have to input; Int, Rand, 1(580,30) for the girls and change the
580 to 603 for the boys. This then means that the calculator will give
me 30 whole numbers within the range of 1-580 or 1-603. This is the
random sample that I obtained;

Girls Boys

Year

Height (m)

Weight (kg)

Year

Height (m)

Weight (kg)

7

1.62

40

7

1.48

44

7

1.63

60

7

1.59

45

7

1.30

36

7

1.50

50

7

1.20

38

7

1.53

40

7

1.43

45

7

1.52

47

7

1.42

29

7

1.55

45

8

1.55

42

8

1.55

51

8

1.72

50

8

1.50

32

8

1.61

52

8

1.90

60

8

1.59

38

8

1.82

64

8

1.70

50

8

1.75

80

8

1.61

60

8

1.72

46

8

1.57

52

8

1.52

43

8

1.56

47

8

1.32

47

8

1.62

51

8

1.50

39

8

1.42

29

9

1.66

54

9

1.65

49

9

1.61

38

9

1.62

45

9

1.54

60

9

1.67

51

9

1.53

45

9

1.54

45

9

1.65

48

9

1.59

45

9

1.80

70

9

1.68

47

9

1.62

52

10

1.73

51

9

1.80

51

10

1.70

60

10

1.66

70

10

1.63

48

10

1.60

47

10

1.62

42

10

1.80

54

10

1.58

45

10

1.63

50

10

1.60

50

11

1.91

82

11

1.55

36

11

1.8

60

11

1.68

48

11

1.86

80

I need a more useful representive of the data shown above, so I have
decided to sort my data out and put it into height and weight
frequency tables. As I will be able to see the data far more clearly
and it will allow me to plot graphs from the data with less
difficulty.

Weight Frequency Tables

Girls Boys

Weight, w (kg)

Frequency

Weight, w (kg)

Frequency

20 â‰¤ w <30

2

20 â‰¤ w <30

0

30 â‰¤ w <40

4

30 â‰¤ w <40

3

40 â‰¤ w <50

13

40 â‰¤ w <50

11

50 â‰¤ w <60

8

50 â‰¤ w <60

7

60 â‰¤ w <70

3

60 â‰¤ w <70

4

70 â‰¤ w <80

0

70 â‰¤ w <80

2

80 â‰¤ w <90

0

80 â‰¤ w <90

3

Height Frequency Tables

Girls Boys

Height, h(cm)

Frequency

Height, h(cm)

Frequency

120 â‰¤ h <130

1

120 â‰¤ h <130

0

130 â‰¤ h <140

1

130 â‰¤ h <140

1

140 â‰¤ h <150

3

140 â‰¤ h <150

1

150 â‰¤ h <160

8

150 â‰¤ h <160

11

160 â‰¤ h <170

13

160 â‰¤ h <170

7

170 â‰¤ h <180

4

170 â‰¤ h <180

2

180 â‰¤ h <190

0

180 â‰¤ h <190

6

190 â‰¤ h <200

0

190 â‰¤ h <200

2

Because both height and weight are continuous data, I have chosen to
group the data in class intervals of tens as this allows me to handle
large sets of data more easily and will be easier to use when plotting
graphs. In both the height and weight column, '120 â‰¤ h <130', this
means '120 up to but not including 130', any value greater than or
equal to 120 but less than 130 would go in this interval. I feel I am
now at the stage where I can go on to record my results in graph form.
This will then allow me to analyse my data and compare the results for
the differing genders, which I am unable to do with the tables above.

Weight

As I mentioned earlier both height and weight are continuous data so I
cannot use bar graphs to represent it, instead I will have to use
histograms as this is a suitable form of graph to record grouped
continuous data. Before I produce the graph I am going to make another
hypothesize that;

"Boys will generally weigh more than girls."

Histogram of boys' weights

[IMAGE]

Histogram of girls' weights

[IMAGE]

Obviously by looking at the two graphs I can tell there is a contrast
between the girls' and boys' weights, but to make a proper comparison
I will need to plot both sets of data on the same graph. Plotting two
histograms on the same page would not give a very clear graph, which
is why I feel by using a frequency polygon it will make the comparison
a lot clearer.

Frequency polygons for boys' and girls' weights

[IMAGE][IMAGE][IMAGE]

This graph does support my hypothesis, as it shows there were boys
that weighed between 80kg and 90 kg, where as there were no girls that
weighed past the 60kg-70kg group. Similarly there were girls that
weighed between 20kg and 30kg were as the boys weights started in the
30kg-40kg interval. Although by looking at my graph I am able to work
out the modal group, but it is not as easy to work out the mean, range
and median also. To do this I have decided to produce some stem and
leaf diagrams as this will make it very clear what each aspect is, for
the main reason I will be able to read each individual weight - rather
than look at grouped weights. Stem and leaf diagrams show a very clear
way of the individual weights of the pupils rather than just a
frequency for the group-which can be quite inaccurate.

Girls Boys

Stem

Leaf

Frequency

Stem

Leaf

Frequency

20 kg

9,9

2

20 kg

0

30 kg

6,6,8,8

4

30 kg

2,8,9

3

40 kg

0,2,2,5,5,5,5,5,7,7,8,8,9

13

40 kg

0,3,4,5,5,5,6,7,7,7,8

11

50 kg

0,0,0,1,1,1,2,2

8

50 kg

0,0,1,1,2,4,4

7

60 kg

0,0,0

3

60 kg

0,0,0,4

4

70 kg

0

70 kg

0,0

2

80 kg

0

80 kg

0,0,2

3

From this table I am now able to work out the mean, median, modal
group (rather than mode because I have grouped data) and range of
results. This is a table showing the results for boys and girls;

Weights (kg)

Mean

Modal Class

Median

Range

Boys

50 kg

40-50 kg

50 kg

50 kg

Girls

46 kg

40-50 kg

47 kg

31 kg

(NB. The values for the mean and median have been rounded to the
nearest whole number.)

Despite both boys and girls having the majority of their weights in
the 40-50kg interval, 13 out of 30 girls (43%) fitted into this
category where as only 11 out of 30 (37%) boys did which is easily
seen upon my frequency polygon. I could not really include that in
supporting my hypothesis as the other aspects do. My evidence shows
that the average boy is 4kg heavier than that of the average girl, and
also that the median weight for the boys are 3kg above the girls.
Another factor my sample would suggest is that the boys' weights were
more spread out with a range of 50kg rather than 31kg as the girls
results showed. The difference in range is also shown on my frequency
polygon where the girls weights are present in 5 class intervals,
where as the boys' weights occurred in 6 of them.

Height

I am now going to use the height frequency tables to produce similar
graphs and tables as I have done with the weight. Obviously as height
is continuous data, as mentioned already, I am going to use histograms
to show both boys and girls weights. I am also going to make another
hypothesis that;

"In general the boys will be of a greater height than the girls."

Histogram of boys' heights

[IMAGE]

Histogram of girls' heights

[IMAGE]

Similarly as with the weight, I can see the obvious contrasts between
the boys' and girls' heights, but the data is not presented in a
practical way to perform a comparison, that is why I am going to put
the two data sets on a frequency polygon.

[IMAGE]Frequency Polygon of Boys' and Girls' Heights

[IMAGE][IMAGE]

This graph does support my hypothesis as the boys' heights reach up to
the 190-200cm interval, where as the girls' heights only have data up
to the 170-180 cm group. Similarly there were girls that fitted into
the 120-130cm category where as the boys' heights started at
130-140cm. As this data is presented in

Girls Boys

Stem

Leaf

Frequency

Stem

Leaf

Frequency

120 cm

0

1

120 cm

0

130 cm

0

1

130 cm

2

1

140 cm

2,2,3

3

140 cm

8

1

150 cm

4,5,5,6,7,8,9,9

8

150 cm

0,0,0,2,2,3,3,4,5,5,9

11

160 cm

0,1,1,2,2,2,2,3,3,5,7,8,8

13

160 cm

0,1,2,3,5,6,6

7

170 cm

0,0,2,3

4

170 cm

2,5

2

180 cm

0

180 cm

0,0,0,0,2,6

6

190 cm

0

190 cm

0,1

2

With these more detailed results, I can now see the exact frequency of
each group and what exact heights fitted into each groups, as you
cannot tell where the heights stand with the grouped graphs. For all I
know all of the points in the group 140 â‰¤ h <150 could be at 140cm,
which is why I feel it is a sensible idea to see exactly what data
points you are dealing with. I can also now work out the mean, median
and range or the data, these are the results I worked out;

Heights (cm)

Mean

Modal Class

Median

Range

Boys

164 cm

150-160 cm

162 cm

59 cm

Girls

158 cm

160-170 cm

161 cm

53 cm

Differing from the results from my weight evidence, the heights' modal
classes for boys and girls differ, and much to my surprise the girls'
modal class is in fact one group higher than the boys. This is very
visible on my frequency polygon as the girls data line reaches higher
than that of the boys. This doesn't exactly undermine my hypothesis
however as the modal class only means the group in which had the
highest frequency, not which group has a greater height. On the other
hand the average height supports my prediction as the boys average
height is 6 cm above the girls. The median height had slightly less of
a difference than the weight as there was only one centimetre between
the two, although again it was the boys' median that was higher. When
it comes to the range of results, similarly to the weight the boys
range was vaster than the girls, although there was no where near as
greater contrast in the two with a difference of only 6 cm between the
two. With all of the work I have done so far, my conclusions are only
based on a random sample of 30 boys and girls so they are not
necessarily 100% accurate, and therefore I will extend my sample later
on in the project. Before I go on to further my investigation, I feel
that it is necessary for me to work out the quartiles and medians of
both data sets, as this allows me to work with grouped data rather
than individual points as in my stem and leaf diagrams. To do this I
am going to produce cumulative frequency graphs as this is a very
powerful tool when comparing grouped continuous data sets and will
allow me to produce a further conclusion when comparing height and
weight separately. I am also going to produce box and whisker diagrams
for each data set on the same axis as the curves for this allows me to
find the median and lower, upper and interquartile ranges very simply
(I have attached a small sheet explaining how I can find these results
from the graphs I am going to produce). I am firstly going to look at
weight, and to produce the best comparison possible I am going to plot
boys, girls and mixed population on one graph.

Cumulative frequency curves for weight

[IMAGE]

All three of my curves clearly show the trend towards greater weights
amongst boys and girls. From looking at my box and whisker diagrams I
have obtained the following evidence:

Weight (kg)

Median

Lower Quartile

Upper Quartile

InterquartileRange

Mean

Mixed

49

43

58

15

51

Boys

51

44

64

20

55

Girls

47

41

54

13

47

These results continue to agree with my prediction made earlier that
the boys will be of a heavier weight than the girls. I can see this as
the lower quartile, upper quartile and mean are all of lower values
than the boys, but also the boys' range of weights is shown to be
greater from these results as their interquartile range is two kg
higher than the girls.

Cumulative frequency for heights

[IMAGE]

These results also show the trend towards a greater height amongst the
boys and girls. Similarly as done with my weight diagram, I have
obtained the following evidence;

Height (cm)

Median

Lower Quartile

Upper Quartile

InterquartileRange

Mean

Mixed

162

154

170

16

163

Boys

163

155

181

26

166

Girls

162

153

167

14

159

Similarly as with the weight results, these results continue to
further my prediction that the boys would be of a greater height than
the girls. As with the weight results this can be seen from the lower
quartile, upper quartile and mean points which in the girls' case are
all of a value smaller than the boys.

From all of the graphs and tables I have produced so far, I can fairly
confidently say that the boys weights' and heights' are higher than
the girls but none of my evidence collected so far helps me conclude
my original hypothesis made; "The taller the pupil, the heavier they
will weigh."

Although when looking at my cumulative frequency graphs of height and
weight, I could make the statement that both diagrams appear to be
very similar from appearance although I cannot make any form of
relationship between the height and weight. I am now going to extend
my investigation and see how height and weight can be related, and to
do this the most effective way is by producing scatter diagrams. I
will plot boys and girls on separate graphs as I feel the results will
produce a stronger correlation when done this way and also to continue
with the style I have begun with. Using scatter diagrams allows me to
compare the correlations of the two graphs, and the equations of the
lines of best fit (best estimation of relationship between height and
weight) of each gender.

Boys' Scatter diagram of height and weight

[IMAGE]

This graph shows a positive correlation between height and weight, and
all of the datum points seem to fit reasonably close to the line of
best fit. There are a few points that I have circled which do not
really fit in with the line of best fit - these are called anomalous
points, it means that they do not fit in with the trend of the
results.

Girls' Scatter diagram of height and weight

[IMAGE]

This graph similarly shows a positive correlation, although the
correlation is stronger than the boys as the spread is greater on the
boys graph than on the girls. The datum points on this graph are quite
closely bunched together in the middle where as on the boys graph
there is a wider spread of results - which would agree with the
conclusion made earlier that the boys' heights and weights are of a
larger range than the girls. I have again circled the anomalous points
on this graph to show which data did not fit in with the trend of
results. As both of my lines of best fit are completely straight, I
would assume that the equation of the line would be in the form of;

y = mx + c.Wheny represents height in cm, and x represents weight in
kg, the equations of the lines of best fit for my data set are (I
obtained these equations from my graphs in autograph as an exact
result was available, however if I were to find the results myself I
would do so by finding the gradients and looking at the point where
they intercept the y axis, NB. attached is a small diagram of how I
would do so):

Boys: y = 0.8004x + 121.6 Girls: y = 0.7539x + 123.6

These equations can be used to make prediction of either weight when
you know the height or vice versa. For example, if I were to predict
the weight of a girl who is 165 cm tall this is what I'd do:

[IMAGE]y = 0.7539x + 123.6 so, x = y - 123.6

0.7539

[IMAGE]If y = 165 cm then x = 165 - 123.6 = 55.91

0.7539

Therefore I would predict a girl of 165 cm would weight 56 kg
(rounding up to a whole number as used on my graphs and data tables)
when using the equations from my lines of best fit. I have checked
this, by lightly drawing a pencil line on my graph across from 165 cm
up to where it meets on the line of best fit and then dragging it down
to the x axis, and after doing so the line met the x axis at around 56
kg.

I have now reached a point in my investigation where my random sample
of 30 boys and girls is not necessary anymore. There have definitely
which have all in fact fitted in with my predictions made. However my
predictions are only based on general trends observed in my data, and
in both the girls and boys samples there were individuals whose
results did not fit in with the general trend. I cannot have complete
confidence in my results so far due to the fact this is only a random
sample of 30 girls and boys and age has not been considered which I
now feel is a necessary factor. I have spent a good amount of time
considering different genders but now I am going to look at age
differences. It is only common sense that age is going to affect your
height and weight, for you would think a year 7 pupil would be smaller
and lighter than a pupil in year 11. As Mayfield is a growing school
there would be more pupils in year 7 than in year 11, therefore my
random sample was likely to contain more year 7 pupils than year 11 -
this is biased and unfair. To ensure that I obtain a data set with an
accurate representation of the whole school, I am going to have to
take a stratified sample. Stratified sample means that you sample a
certain amount from a particular group to proportion that group's size
within the whole population, i.e. pupils within year 8, within the
whole school.

This is a table showing the number of girls and boys in each year at
Mayfield:

Girls

Boys

Total

% of WholeSchool

Year 7

131

151

282

24%

Year 8

125

145

270

23%

Year 9

143

118

263

22%

Year 10

94

106

200

17%

Year 11

86

84

170

14%

I have decided to continue with a sample of 60 pupils, 30 girls and 30
boys, as I feel from my random sample this amount of data was easy to
work with and produced some sufficient results. I have now got to work
out how many girls and boys I will need from each year to make sure
that my sample is a good representation of the whole school. To do
this, I must consider the boys and girls separately as there are 580
girls in the school and 603 boys. When working out the year 7 sample
this is what I'd do;

Take the total number of year 7 girls-131, and divide that by the
total number of girls in the school, 580 â€¦

131/580 = 0.22586207â€¦I then have to multiply that number by 30 as that
is the total number of girls data I wish to obtain â€¦ 0.22586207 X 30 =
6.7758621 â€¦ if I then round that number up to one whole number it
means that I need 7 girls from year 7 in my stratified sample.

This is the calculations performed to retrieve my stratified sample
numbers;

Year 7 - Girls - 131/580 = 0.22586207 X 30 = 6.7758621 = 7

Year 7 - Boys - 151/603 = 0.25041459 X 30 = 7.5124377 = 8

Year 8 - Girls - 125/580 = 0.21551724 X 30 = 6.4655172 =6

Year 8 - Boys - 145/603 = 0.24046434 X 30 = 7.2139302 = 7

Year 9 - Girls - 143/580 = 0.24655172 X 30 = 7.3965516 = 7

Year 9 - Boys - 118/603 = 0.19568823 X 30 = 5.8706469 = 6

Year 10 - Girls - 94/580 = 0.16206897 X 30 = 4.8620691 = 5

Year 10 - Boys - 106/603 = 0.17578773 X 30 = 5.2736319 = 5

Year 11 - Girls - 86/580 = 0.14827586 X 30 = 4.4482758 = 5

Year 11 - Boys - 84/603 = 0.13930348 X 30 = 4.1791044 =4

Despite my new sample of 60 being stratified, to obtain the particular
number of girls and boys from each year, I am going to select them
randomly so again no biased is shown. I selected my random pupils
using my calculator by performing; (year 7 girls) SHIFT RAN# X 131,
I'd repeat this 7 times until I had 7 sets of data. This was obviously
repeated for all years but changing the number it was multiplied by
depending on how many pupils there were in each group.

Using my new stratified sample, I produced a scatter graph for each
age and alternate gender, i.e. a boys and girls scatter graph for year
7,8,9,10,11. I am going to maintain the same hypothesis of "the
greater the height, the greater the weight, but I can also comment on
the older the pupil the greater the height or weight."

Year 7

Boys

[IMAGE]

Girls

[IMAGE]

For the year 7 graphs, the lines of best fit appear to be at a similar
slope to one another although the boys begin at a higher point on the
y axis than the girls - which would determine that the boys were
taller. The boy's points appear more spread out but closer to the line
of best fit, where as the girls are more sparsely distributed but are
situated quite closely together on the line area. Both lines have a
positive correlation which would agree with the taller the person the
heavier they weigh.

Year 8

Boys

[IMAGE]

Girls

[IMAGE]

Differing from the year 8 graphs the lines of best fit are at quite
different gradients. These graphs show that the boys in year 8 follow
a strong pattern, of the taller you are the heavier you weigh - shown
by the positive correlation of the line. However the girls graph
differs and has a very slight correlation which could be for many
reasons - one being that girls watch their weight slightly more. The
points on both of these graph are more sparsely distributed around the
lines of best fit, where as the year 7 points were more closely
grouped together. This could be for the reason that your body starts
to change in many different ways as you grow older.

Year 9

Boys

[IMAGE]

Girls

[IMAGE]

The Year 9 graphs show greater contrast again, although of a similar
pattern to the year 8 ones. The boys shows an even steeper positive
correlation showing the heavier you weigh the taller you are, and
similarly the girls show the line of best fit almost positioned
horizontally across the page. Both of these graphs have points
positioned very closely to the line of best fit, although that could
just be coincidence.

Year 10

Boys

[IMAGE]

Girls

[IMAGE]

The year 10 graphs show a complete change with both of the graphs
consisting of a practically horizontal line of best fit, the girls
could be explained due to this gender caring about their appearance
more, but the boys change I cannot explain. This could just be a
fluke, as there are only 5 points on the graph anyway - which is a
small percentage of all the year 10 boys.

Year 11

Boys

[IMAGE]

Girls

[IMAGE]

The small amount of data points on these graphs is barely enough for
me to make a conclusion, however the boys graphs shows again the
positive correlation as before. But the girls' graphs differ again and
now create a negative correlation which would predict that the taller
you are the less you weigh.

Although these graphs have given me some points to consider, one being
why the girls graphs tend not to consist of "the taller you are the
heavier you weigh" as the age increases. I have come to the conclusion
that because as girls reach puberty and start developing they become
more aware of their appearance and therefore try to watch their weight
a bit more. Although, I only had a small stratified sample to
represent the whole school, so it would not be an accurate source of
information to draw an efficient conclusion from. However I did
produce this table from all of my data points to see whether a further
pattern occurred:

Year 7

Year 8

Year 9

Year 10

Year 11

Girls

Boys

Girls

Boys

Girls

Boys

Girls

Boys

Girls

Boys

Median height (cm)

151

156

157

165

165

166

156

166

165

169

Mean height (cm)

150

155

154

168

164

165

158

168

164

170

Range of heights (cm)

18

15

20

14

12

25

14

25

14

20

Median weight (kg)

41

47

44

51

50

48

60

56

54

56

Mean weight (kg)

44

48

47

49

49

48

54

56

56

55

Range of weights (kg)

14

25

51

34

17

17

29

25

16

30

The only part of the table that I can assume a conclusion from is the
mean as, when the age increases the weight and height does so to.
Apart from a couple of irregular points further up the school there is
a slight trend in the average heights and weights.

Seeing as I didn't have a big enough sample to make any meaningful
statements within the data, I have decided to further my investigation
again and to look in more detail at just one year group to see whether
I can draw a better conclusion from these results. I have decided to
look at each year group in more detail, however I am only going to
write up an example using year 9 girls as I do not feel it is
necessary for me to show each one in full. I am going to extract a
random sample which will add up to 10% of the total girls in year 9.
As there are 143 girls in year 9 at MayfieldHigh School, I will need a
total of 14 pupils; this is the random sample I extracted;

Height (cm)

152

162

180

163

153

155

150

157

170

165

164

178

161

162

Weight (kg)

45

52

60

47

52

66

45

62

48

72

40

59

52

58

I can create a brief summary of the heights and weights in a table, as
I have done with the majority of my other samples although I also used
graphs with these, these is my summary;

Median Weight (kg)

52

Mean Weight (kg)

54

Rangeof Weights(kg)

32

Median Height (kg)

162

Mean Height (kg)

162

Rangeof Heights(kg)

30

From this data, although I have considered the range of results there
is another measure of spread which I have not yet considered in my
project is standard deviation. Thisis the measure of the scatter of
the values about the mean value also thought of as a measure of
consistency. Standard deviation uses the square of the deviation from
the mean, therefore the bigger the standard deviation the more spread
out the data is. I am firstly going to work out the standard deviation
of the year 9 girl's heights' where 'x'represents the heights. To find
the standard deviation using the equation;

we need to first work out the mean value, then square each value and

these squares. I have put my values in a table as it is easier to keep
track

of them then.

x (cm)

xÂ² (cmÂ²)

152

23104

162

26244

180

32400

163

26569

153

23409

155

24025

150

22500

157

24649

170

28900

165

27225

164

26896

178

31684

161

25921

162

26244

âˆ‘x=2272

âˆ‘xÂ²=369'770

I am also going to work out the standard deviation of the girl's
weights, I am going to use the same method, and the only difference
being that 'x' now represents weight rather than height.

x (kg)

xÂ² (kgÂ²)

45

2025

52

2704

60

3600

47

2209

52

2704

66

4356

45

2025

62

3844

48

2304

72

5184

40

1600

59

3481

52

2704

58

3364

âˆ‘x=758

âˆ‘xÂ²=42'104

These are the results I obtained for the standard deviation for each
year group - boys and girls separately;

Year

Gender

Mean height (cm)

S.D for height (cm)

Mean weight (kg)

S.D for weight (kg)

7

Boys

Girls

154

147

12

15

47

43

9

7

8

Boys

Girls

163

155

19

13

49

45

15

7

9

Boys

Girls

168

162

17

13

52

54

6

10

10

Boys

Girls

169

163

31

11

59

51

6

5

11

Boys

Girls

176

164

12

12

64

55

12

9

From looking at the mean averages for each separate gender set, the
boys' height and weight increase as the age increases. The biggest
increase for the boys' height was from year 7-8 where the average
height increased 9cm, from 154cm up to 163cm. Although when looking at
the weight increases, it appears there is a slightly more even
increase however the biggest jump is 7kg from year 9-10. The girls
results' generally appears to increase as their age increases,
although there is one fault in the weight section. The girls' heights
increase most rapidly from years 7-9 where the height increases 15cm
on average (147cm-162cm); although from years 9-11 there is only a
minute increase of 2 cm, a centimetre for each year. This could be
because girls develop earlier than the boys and therefore grow faster
when they are younger, and slow down when they become older. However,
when looking at the weight there is one decrease in the average weight
as the age increases, from year 9-10 there is a deduction of 3kg, from
54kg-51kg. This could be because this is the prime age when girls
start to become far more concerned about their appearance and
therefore watch their weight. Despite this one fault, these results
would agree with my hypothesis made earlier that the older you are the
heavier/taller you will be. When looking at the boys and girls
results' together, in each case apart from one, the boys' average
height/weight is higher than that of the girls. There is only one
point that undermines this pattern, and that is for the weight of the
year 9 pupils, where the girls average weight is 2 kg more than the
boys.

When looking at the standard deviation it shows that the year 11
pupils' heights on whole has the highest level of consistency, with an
equal 12 cm deviation for both sexes. Although when looking at the
weight the boys in year 11 maintained a deviation of 12 kg for their
weight, however the girls' weights proved to be more consistent with a
deviation of 9 kg. In general with the weight, the boys' standard
deviation is higher than the girls with an average of 3.5 kg
difference above them. The only year which differs from this is again
the year 9 group - where the girls standard deviation is 4 kg above
the boys, this could be related to the girls average weight being
heavier than the boys in this section also. I could now say that the
girls' weights' are in general more consistent and therefore the data
points have a smaller measure of spread.

The heights standard deviation does not show much of a pattern,
however in years 8,9,10 the standard deviation is higher for the boys
than it is for the girls with an average increase of 10 cm difference
above the girls. This great difference could be because of the
irregular high value of 31cm standard deviation for the year 10 boys,
where as the girls only had 11cm. This high value means that the
heights for the boys in this year group are quite irregular, and there
is a vast measure of spread - I can not see a reason for this however
I have to keep in mind this is only a 10% sample of the whole year
group therefore it could be that the values selected were just
coincidentally a large range of heights. When looking to see if there
was any pattern in the standard deviations as the age differs, the
girls proved to consist of a slight pattern. From year 7-11 the
standard deviation values consisted of; 15cm, 13cm, 13cm, 11cm, 12cm -
which shows a general decrease as the pupils grow older, despite the
one centimetre increase from year 10-11. All of these values are all
very close to each other (within 4 cm of one another), where as the
boys values differ slightly more with 12cm, 19cm, 17cm, 31cm, and 12cm
(year 7-11). The only conclusion I can draw from this is that the
girls heights are overall far more consistent than the boys, and it
could be that as the girls increase in age the standard deviation
becomes less (more consistent), and the spread of the data points
become closer.

Before making a final summary of my findings throughout this
investigation, I am going to briefly look at one more factor to
compare height and weight to, and that is the 'Body Mass Index'. A
body mass index defines whether you are underweight, healthy,
overweight or obese by calculating; kg/mÂ² = BMI.

You can tell whether you are underweight, normal, overweight or obese
from the number these are the categories ; Under 17 = underweight

17-25 = normal (between 17 and 22 you are expected to live a longer
life)

25-29.9 = overweight

Over 30 = obese

Using a new random sample of 60 pupils girls and boys, I have worked
out the BMI for each of the pupils and produced a graph comparing the
BMI and weight, and the BMI and height. One prediction I would make is
"The heavier the person, the higher the BMI."

Boys Weight compared to BMI

[IMAGE]

Boys height compared to BMI

[IMAGE]

Girls weight compared to BMI

[IMAGE]

Girls height compared to BMI

[IMAGE]

From looking at the graphs, it proves to be that weight is the greater
factor when considering the BMI. I know this as both of the weight
graphs for each sex, show that the data points create a positive
correlation which would suggest that the heavier the pupil the higher
their body mass index - supporting my prediction made. Despite the
differing genders, the slope of the line of best fit appears to be
very similar although there are far more anomalous points upon the
boys graph rather than the girls. When considering height, there
appears to be no relationship between the two factors as the data
points are scattered everywhere upon the page. However similar to the
weight, the girls data points appear to be more sparsely populated
around the line of best fit than the boys. From these graphs you could
also say that the girls' heights and weights are more consistent than
the boys.

Additionally I'm going to obtain 10 pupils heights and weight from
each year - 5 boys and 5 girls, then I will work out each of their BMI
and come up with an average BMI for each separate sex in each year
group. I am going to work out one of the pupils just to explain how
you work it out. Take for example a boy from year 7, he weighs 47 kg
and is 149 cm tall, therefore the calculation for his BMI would be;

47 Ã· 1.49Â² = 21.2 â€¦ therefore this boy is in the normal range

This is a table showing the average BMI for each year group (boys and
girls);

Boys average BMI

Girls average BMI

Year 7

20.0

18.9

Year 8

21.2

20.6

Year 9

22.1

20.8

Year 10

22.4

21.4

Year 11

23.1

22.0

As you can the average BMI for each gender and age group is in the
normal/healthy range. The BMI doesn't in fact say, the heavier you are
the more your BMI will be, all it states is when you compare your
height and weight whether you are normal, underweight, overweight or
obese. However there is a pattern occurring within these results, that
being that all of the boys BMI's are higher than the girls and also
the older that both sexes get, the higher the BMI increases. This
would not necessarily happen in all cases, as you could have 5 obese
year sevens' in one group and 5 underweight pupils in another group,
but coincidentally it has proved to be as your age increase the BMI
does also. This could be because you do tend to gain weight far easier
as you get older, also because you are growing until around
approximately 16-18 years. Knowing that all of these average body mass
index results are in the healthy range it would suggest that
MayfieldHigh Schoolis in a good area and the children that attend the
school live in reasonable conditions. However if all of the results
were either underweight or obese, I could suggest that the school may
be situated in a deprived area - and children are either not fed
properly or over eat from depression or boredom. This is only a very
rough suggestion but it could be a possible outcome.

Throughout this project I have made many hypothesise including;

1) The heavier the pupil, the taller they will be

2) In general boys will weigh more than girls

3) In general boys will be of a greater height than girls

4) The older the pupil the greater the height/weight

5) The heavier the pupil the higher the BMI will be

I have answered all of these predictions throughout the project with
either graphs or text, and it is proved that all of my hypothesise
made have been in general correct. There have been some slight points
which undermine the predictions, but all over they have been
successful. My original task was to compare height and weight,
although I have not only considered height and weight but including
biased factors such as gender and age. Additionally to this, I have
also introduced another factor - being the body mass index to see
whether height and weight have any relationship to the BMI values of
students. As mentioned above, my graphs show that weight does have a
relationship with the BMI, where as height does not appear to.

When considering age as a biased factor, I produced a stratified
sample trying to create a suitable representation of the school on a
smaller scale. Using the data for this stratified sample my results
proved that in general the older you are the heavier/taller you are,
however there was a group of pupils in year 9 which undermined this
prediction. These results are however not 100% effective due to there
only being a very minimal amount of data for each year group and
gender.

Despite considering the age factor, I also spent a great deal of time
looking at the differing genders to see whether that affected the
height and weight of pupils at all. When looking at this I produced
histograms, frequency polygons, cumulative frequency graphs and box &
whisker diagrams, stem & leaf diagrams and scatter diagrams. The
overall conclusion was that boys in general are of greater height and
weight - mainly defined by the mean values which were higher than that
of the girls.

However, all of these hypothesise were all as a part of my main
prediction; "The taller the pupil the heavier they will weigh", and
from answering all of these other predictions I can confidently say
that it is true. I have come to this conclusion based on all of the
graphs, diagrams, tables and statements made. On the other hand there
were cases where certain data undermined this prediction but that
could have been because of the small samples I had allocated myself to
obtain. When producing the random sample of 60, I felt that was a
satisfactory amount to work with as picking up an analysis and
producing graphs from this data was simple and done efficiently.
Although when it came to the stratified sample, and I was looking at
the different age groups using again a sample of 60 trying to
represent the school on a smaller scale - I do not feel it was as
successful. If I were to repeat or further this investigation - I
would definitely use a larger number of pupils for the stratified
sample as when the numbers of the school pupils were put on a smaller
scale, I only ended up in some cases with a scatter graph with only 4
datum points upon for the year 11 students. To retrieve accurate
results from this method of sampling, I feel it is necessary to use a
sample of at least 100. Additionally to the stratified work, if I had
a larger sample - I would also produce additional graphs, i.e.
cumulative frequency/ box and whisker, as I feel that I could draw a
better result from these as I felt the scatter diagrams I produced
were rather pointless.

I feel my overall strategy for handling the investigation was
satisfactory, if I had given myself more time to plan what I was going
to do I think I would have come up with a better method and possibly
more successful project. One of the positive points about my strategy
is that because I used a range of samples it meant that I was not
using the same students' data throughout - I instead used a range of
data therefore maintaining a better representative of Mayfied school
on a whole. There is definitely room for improvements for my
investigation - if I were to do it again I would spend a lot more time
planning what I was going to do instead of starting the investigation
in a hurry. Despite that I feel my investigation was successful as it
did allow me to pull out conclusions and summaries from the data used.

MLA Citation:
"Interpreting Data - Relationship Between Weight and Height." 123HelpMe.com. 10 Dec 2013
<http://www.123HelpMe.com/view.asp?id=120990>.