Investigating the Relationship Between Height and Weight of Students
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Investigating the Relationship Between Height and Weight of Students
Collecting the data Mayfield High School is a school for 1116 year olds. The line of inquiry, which I will use to investigate the school, is the relation between height and weight. I will take a random sample of the school by giving each student a number and creating a random number between 0 and 1 using the random number button on my calculator (RAN#). Then I will multiply this number by 1183 to create a number between 1 and 1183. I will do this until I get a sample of 30 boys and 30 girls. The Data · Number0.89 x 1183 = 1052.87 = 1053 (f) · Number0.476 x 1183 = 563.108 = 563 (f) · Number  0.95 x 1183 = 1123.85 = 1124 (m) · Number  0.855 x 1183 = 859.74525 =860 (m) · Number  0.678 x 1183 = 802.074 =802 (m) · Number  0.611 x 1183 = 722.813 =722 (m) · Number 0.071 x 1183 = 83.993 = 84 (f) · Number  0.651 x 1183 = 770.113 = 770 (m) · Number  0.993 x 1183 = 1174.719 = 1175 (m) · Number  0.856 x 1183 = 1012.648 = 1013 (f) · Number  0.692 x 1183 = 818.636 = 819 (f) · Number  0.935 x 1183 = 1106.105 = 1106 (f) · Number  0.52 x 1183 = 615.16 = 615 (m) · Number  0.981 x 1183 = 1160.523 = 1161 (m) · Number  0.58 x 1183 = 686.14 = 686 (m) · Number  0.348 x 1183 = 411.684 = 412 (m) · Number  0.24 x 1183 = 283.92 = 284 (m) · Number  0.564 x 1183 = 667.212 = 667 (m) · Number  0.975 x 1183 = 1153.425 = 1153 (m) · Number  0.426 x 1183 = 503.958 = 504 (m) · Number  0.803 x 1183 = 949.949 = 950 (m) · Number  0.47 x 1183 = 556.01 = 556 (m) · Number  0.815 x 1183 = 964.145 = 964 (f) · Number  0.747 x 1183 = 883.701 = 884 (f) · Number  0.185 x 1183 = 218.855 = 219 (m) · Number  0.266 x 1183 = 314.678 = 315 (f) · Number  0.12 x 1183 = 141.96 = 142 (m) · Number  0.768 x 1183 = 908.544 = 909 (m) · Number  0.667 x 1183 = 789.061 = 789 (m) · Number  0.345 x 1183 = 408.135 = 408 (f) · Number  0.936 x 1183 = 1107.288 = 1107 (f) · Number  0.534 x 1183 = 631.722 = 632 (f) · Number  0.285 x 1183 = 337.155 = 337 (f) · Number  0.575 x 1183 = 680.225 = 680 (m) · Number  0.237 x 1183 = 280.371 = 280 (m) · Number  0.471 x 1183 = 557.193 = 557 (m) · Number  0.837 x 1183 = 990.171 = 990 (f) · Number  0.269 x 1183 = 318.227 = 318 (f) · Number  0.193 x 1183 = 228.319 = 228 (f) · Number  0.457 x 1183 = 540.631 = 541 (m) · Number  0.533 x 1183 = 630.539 = 631 (m) · Number  0.27 x 1183 = 319.41 = 319 (m) · Number  0.19 x 1183 = 224.77 = 225 (m) · Number  0.377 x 1183 = 445.991 = 446 (f) · Number  0.639 x 1183 = 755.937 = 756 (m) · Number 0.676 x 1183 = 799.708 = 800 (f) · Number  0.57 x 1183 = 674.31 = 674 (f) · Number  0.127 x 1183 = 150.241 = 150 (m) · Number  0.927 x 1183 = 1096.641 = 1097 (f) · Number  0.329 x 1183 = 389.207 = 389 (m) · Number  0.572 x 1183 = 676.676 = 677 (m) · Number  0.172 x 1183 = 202.293 = 202 (f) · Number 0.955 x 1183 = 1129.765 = 1130 (f) · Number  0.963 x 1183 = 1139.229 = 1139 (f) · Number  0.941 x 1183 = 1113.203 = 1113 (f) · Number0.868 x 1183 = 1026.844 = 1027 (f) · Number  0.153 x 1183 = 180.999 = 181 (f) · Number  0.214 x 1183 = 253.162 = 253 (f) · Number  0.203 x 1183 = 240.149 = 240 (f) · Number  0.307 x 1183 = 363.181 = 363 (f) · Number  0.397 x 1183 = 469.651 = 470 (f) · Number  0.491 x 1183 = 580.853 = 581 (f) · Number  0.559 x 1183 = 661.297 = 661 (f) Tables of Data Height (m) Weight (kg) 1.63 38 1.58 36 1.63 52 1.60 45 1.67 52 1.65 59 1.65 54 1.80 50 1.54 50 1.62 46 1.58 72 1.30 36 1.68 50 1.54 54 1.64 40 1.52 50 1.67 48 1.56 63 1.57 52 1.60 54 1.62 35 1.65 59 1.75 50 1.71 54 1.49 53 1.32 48 1.60 46 1.57 52 1.47 38 1.69 42 Boys Girls Height (m) Weight (kg) 1.65 50 1.75 60 1.53 32 1.70 110 1.73 47 1.62 57 1.52 47 1.90 80 1.64 59 1.50 49 1.52 45 1.54 40 1.87 70 1.66 46 1.55 50 1.34 42 1.61 45 1.60 50 1.78 67 1.62 42 1.52 45 1.50 50 1.60 40 1.65 69 1.55 47 1.60 41 1.65 51 1.55 38 1.76 55 1.72 46 Height, h (cm) Frequency 1.201.30 1 1.311.40 1 1.411.50 2 1.511.60 11 1.611.70 12 1.711.80 3 1.811.90 0 Boys Girls Height, h (cm) Frequency 1.201.30 0 1.311.40 1 1.411.50 2 1.511.60 11 1.611.70 9 1.711.80 5 1.811.90 2 Weight, w, kg Frequency 3040 6 4150 11 5160 11 6170 1 7180 1 Weight, w (kg) Frequency 3040 4 4150 16 5160 6 6170 3 7180 0 8190 0 91100 0 101110 1 Heights Graphs [IMAGE] [IMAGE] [IMAGE] The mode height in my sample was higher for girls than boys. The evidence from the sample suggests the range of boys' heights will be larger than the range for girls' heights. Mean height for girls and boys Mean height for boys=all boys' heights/30= 48.73m/30= 1.624m Mean height for girls=all girls' height/30=47.9m/30= 1.596m Modal class interval for girls and boys Modal class interval for boys = 1.511.60m Modal class interval for girls = 1.611.70m Median height for girls and boys Median height for boys= 1.615m Median height for girls = 1.61m Range of heights for boys and girls Range of heights for boys= 1.901.34m=0.56m Range of heights for girls= 1.801.30m=0.5m Height (m) Mean Mode Median Range Boys 1.624m 1.511.60m 1.615m 0.56m Girls 1.596m 1.611.7m 1.61m 0.5m All 3 measurements of average (mean, mode and median) are greater for boys apart from the modal class value. Also the range of heights is slightly larger for boys. In general I believe boys are taller generally as the mean which is often the most accurate average is substantially higher for boys than for girls. Evidence from the data shows that 27/30 boys (90%) are taller than 1.51m while only 25/30 (83%) of girls are taller than 1.51m. [IMAGE] Stem leaf diagram for boys Stem Leaf Frequency 120 0 130 4 1 140 0 150 0, 0, 3, 2, 2, 4, 5, 2, 5, 5 10 160 5, 2, 4, 6, 1, 0, 2, 0, 5, 0, 5 11 170 5, 0, 3, 8, 6, 2 6 180 7 1 190 0 1 Stem leaf diagram for girls Stem Leaf Frequency 120 0 130 0, 2 2 140 7, 9 2 150 8, 4, 8, 4, 2, 6, 7, 7 8 160 3, 3, 0, 7, 5, 5, 2, 8, 4, 7, 0, 2, 5, 0, 9 15 170 5, 1 2 180 0 1 190 0 Weights Graphs [IMAGE] [IMAGE] Mean weight Mean boy's weight= 1570/30=52.3kg Mean girl's weight= 1478kg/30= 42.3kg Modal class interval Modal boy's weight=5160kg Modal girl's weight=4150 and 5160kg Median weight Median boys weight=49.5kg Median girls height=50kg Range of boys and girls weights Range of weights for boys= 11032 kg = 78kg Range of weights for girls= 7236kg=36kg Weight (kg) Mean Modal class interval Median Range Boys 52.3 5160 49.5 78 Girls 42.3 4150 and 5160 50 36 All three measurements for boys and girls were either higher for boys or equal though the range for the boys was double the range of the girls with a range of 78kg to 36k. The evidence suggests that there are many heavy boys as the mean average is quite high and range are high which means that the small number of heavy boys are pushing up the average. [IMAGE] Extension I think that the taller a person, the heavier he or she will weigh. I will test this hypothesis by taking a new sample of 30 students by using the random number function again. 1.82 64 1.51 48 1.68 53 1.50 52 1.55 57 1.50 57 1.53 44 1.56 60 1.54 54 1.84 76 1.62 72 1.59 47 1.41 40 1.68 59 1.55 50 1.48 39 1.62 49 1.6 42 1.32 38 1.67 51 1.54 57 1.42 29 1.72 51 1.71 60 1.68 50 1.60 49 1.62 45 1.55 67 1.55 36 1.63 50 [IMAGE] [IMAGE] A Person [IMAGE] There is a positive correlation between height and weight. This suggests the taller someone is, he more they will weigh. My line of best fit suggests that someone who is 1.6m tall will weigh 52kg. There will be a better correlation it I consider boys and girls separately. Text Box: A Person [IMAGE] [IMAGE] [IMAGE] There is a stronger correlation if boys and girls are considered separately. The line of best fit suggests that a girl of 1.6m would weigh 51kg when a boy of 1.6m would weigh 56kg. Cumulative Frequency Graphs Height, h (cm) Boys Height, h (cm) Girls Height, h (cm) Mixed 1.201.30 0 1.201.30 1 1.201.30 1 1.311.40 1 1.311.40 2 1.311.40 3 1.411.50 3 1.411.50 4 1.411.50 7 1.511.60 14 1.511.60 15 1.511.60 29 1.611.70 23 1.611.70 27 1.611.70 50 1.711.80 28 1.711.80 30 1.711.80 58 1.811.90 30 1.811.90 30 1.811.90 60 [IMAGE] Text Box: [IMAGE] [IMAGE] [IMAGE] Summary of results According to my results, there is a positive correlation between height and weight so therefore tall people will weigh more than short people. Since the points on the boys scatter gram are more dispersed about the line of best fit than for girls. This suggests that the correlation is better for girls and that girls' heights are more predictable than boys. Also the relationships between height and weight do not seem to be linear so a curved line of best fit would be preferred. The cumulative frequency graphs prove that girls are heavier than boys. However I think these correlations will be clearer if I take a stratified sample and analyse the heights by gender and year. Also if I analyse age and create 10% samples for every year group I will get a better set of results. New Hypothesis  I think that that girls will weigh less than boys for the same heights but that girls heights will be more predictable i.e. on the scatter gram the results will be more bunched together and for boys the results will be more spread out e.g. there will be boys at either extremes (some tall, some short). I also think that older people will weigh more than younger people. I will try and prove my hypothesises by taking a stratified sample of the school so that age and gender bias are eliminated and by taking a 10% sample of every year and analysing the data. Stratified samples  A stratified sample means that all the results are in ratio to each other and reflect the spread of people in the school. To do this stratified sample, I will find out what fraction of the population is in each year and base my results on that. By taking a stratified sample you can eliminate bias from gender and age. Year group Number of boys Number of girls Total 7 4 3 7 8 4 3 7 9 3 4 7 10 3 2 5 11 2 2 4 Total 16 14 30 Gender Year group Height(cm) Weight(kg) Male 7 1.54 38 Male 7 1.51 45 Male 7 1.40 40 Male 7 1.49 47 Male 8 1.57 51 Male 8 1.48 40 Male 8 1.72 53 Male 8 1.63 55 Male 9 1.67 60 Male 9 1.70 65 Male 9 1.72 90 Male 10 1.77 80 Male 10 1.57 64 Male 10 1.50 65 Male 11 1.52 45 Male 11 1.51 38 Female 7 1.61 45 Female 7 1.65 45 Female 7 1.42 34 Female 8 1.61 60 Female 8 1.57 45 Female 8 1.58 58 Female 9 1.8 57 Female 9 1.68 57 Female 9 1.51 65 Female 9 1.57 62 Female 10 1.73 42 Female 10 1.80 74 Female 11 1.59 45 Female 11 1.60 55 Mean boy's height = 1.58m Mean boy's weight = 51kg  Modal class interval of height=1.511.6m Modal class interval of weight=3140kg and 5160kg Mean girl's height=1.62m Mean girl's weight=53kg Modal class interval of height= 1.511.6m Modal class interval of weight=4150kg Range of boy's heights= 0.37m Range of boy's weight's= 52kg Range of girl's heights= 0.38m Range of girls weights= 32kg Even now we do not have enough information to make valid statements about each year group. I will rectify this problem by making a 10% sample of each year group. I will start this by taking 10% of the Year 7 pupils. [IMAGE] [IMAGE] Height(m) Mean height: 1.6m ================= Mean weight: 44.7kg Median height: 1.52m Median weight: 43.5kg Modal height: 1.52m Range of heights: 0.29m Range of weights: 44kg Weight(kg) 1.45 43 1.48 44 1.55 53 1.62 48 1.60 40 1.42 26 1.59 45 1.56 53 1.45 40 1.52 40 1.42 Deviation ========= Another way to find the measure of spread is to measure the deviation of a result from the mean. I will do this by subtracting the mean from the height of the person. 41 1.50 41 1.41 45 1.36 38 1.52 37 1.54 43 1.52 25 1.64 50 1.61 45 1.62 40 1.61 47 1.65 45 1.63 45 1.58 50 1.56 35 1.48 42 1.49 38 1.65 69 Year 7 Height (m) The mean deviation for the year 7 pupils is  1.71 which shows many people are below the average height of 1.6m Deviation (m) 1.36 0.24 1.36 0.23 1.41 0.18 1.41 0.18 1.42 0.17 1.42 0.17 1.45 0.14 1.45 0.14 1.48 0.11 1.48 0.11 1.49 0.1 1.5 0.09 1.52 0.07 1.52 0.07 1.52 0.07 1.54 0.05 1.55 0.04 1.56 0.03 1.56 0.03 1.58 0.01 1.59 0 1.6 0.01 1.61 0.02 1.61 0.02 1.62 0.03 1.62 0.03 1.63 0.04 1.64 0.05 1.65 0.06 1.65 0.06 [IMAGE] [IMAGE] Final Summary The stratified sample of 30 students shows there was a mean height for boys of 1.58m and 1.62 for girls. However the range of heights for the boys was much greater than that from the girls. This suggests there will be many boys who are taller than the girl's mean of 1.62 but there will be even more boys who are shorter. The correlation between height and weight is not very clear in year 7 but the correlation is still positive but only slightly positive. To find out a better and more accurate result a sample from every year should be taken. There is also a positive correlation between height and weight across the school but it is strongest when genders and year groups are considered separately. However it seems that the relationship is not linear so a curved line of best fit should be more appropriate but more analysis and sampling is needed for that as the number of people sampled is not very high so a few freak results could upset the whole collection of results e.g. in my main sample there was a girl who was 1.7m tall and 110 kg which changed the scatter gram's line of best fit considerably. How to Cite this Page
MLA Citation:
"Investigating the Relationship Between Height and Weight of Students." 123HelpMe.com. 24 Apr 2014 <http://www.123HelpMe.com/view.asp?id=121649>. 
