# Investigation of Film Lengths

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Investigation of Film Lengths

The title of my investigation is 'The Average Length of a Sample of 52
Randomly Selected Films'. As you can interpret from this title, I am
going to investigate into the length of a set of randomly selected
feature length films. I have chosen to investigate into this topic
because I am a Film Studies student and am required by this subject to
produce a feature length film as part of a coursework assignment. This
leaves me with the predicament of trying to decide how long my feature
film should be. Is there a certain length of film that after the
audience has finished watching, they feel that they have not got their
money's worth and in consequence leave the cinema feeling
disappointed? In contrast, is there a certain length of film that
after the audience has finished watching, they are bored because the
film has run on for too long? In short, my aim for this investigation
is to find the average length of feature films and so enable me to
correctly decide the length of my Film Studies coursework film so that
the audience leaves happy after viewing it.

To determine a population for my course-work, I am going to use the
HMV superstore Internet site to search for my sample of films. This
film site is split up into categories corresponding to letters of the
alphabet; therefore there are a total of 26 categories as there is 26
letters of the alphabet. Each category contains roughly 500 films
giving a total population of 130,00 films. Obviously this population
is far too vast, so I what I propose to do is to number each film in a
category and then the random number generator function on my
calculator to give two random numbers. I then match up the numbers
with the corresponding films, and get two films for each category,
complete with total running time and year of release. I will therefore
end up with a sample of 52 films, fulfilling the criteria of a sample

MLA Citation:
"Investigation of Film Lengths." 123HelpMe.com. 20 Feb 2020
<https://www.123helpme.com/view.asp?id=121395>.

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### Popular Essays

of at least 50 items of single variable data. To ensure that my sample
of films is as accurate as possible, I am going to cross-reference the
data that I collect from the HMV site with data from the Channel 4
Film Four website. Film Four is regarded in film society as being the
definitive movie database, and if this site does not know what you are
looking for, then no one does. I would use this site to originally
collect my data, but it has a smaller total population of films, that
is, its categories do not contain as many films as HMV does. It is
never the less a useful point of cross-reference.

See overleaf for collected data

On this page I have included results that I calculated with the help
of Microsoft Excel. I can then later compare my own calculated results
with those shown below.

Mean

120.1346154

Standard Deviation

28.15296373

1st Quartile

103.75

Median

117.5

3rd Quartile

129.25

To get a visual idea of the spread of my data, I decided to represent
it in a stem and leaf diagram:

70

7

80

8

0

1

5

90

1

2

4

5

3

7

100

5

0

5

5

5

4

3

4

5

110

1

7

4

5

4

4

8

120

9

1

1

0

2

3

0

8

4

5

2

1

130

0

6

9

0

140

7

8

150

6

160

7

4

2

170

180

1

6

190

200

210

3

N = 52 156 6 represents 156 mins.

Stem and Leaf diagram showing the total duration of a sample of 52
films (unsorted)

To help me when constructing a cumulative frequency diagram, I have
sorted the above diagram:

70

7

80

0

1

5

8

90

1

2

3

4

5

7

100

0

3

4

4

5

5

5

5

5

110

1

4

4

4

5

7

8

120

0

0

1

1

1

2

2

3

4

5

8

9

130

0

0

6

9

140

7

8

150

6

160

2

4

7

170

180

1

6

190

200

210

3

N = 52 156 6 represents 156 mins.

Stem and Leaf diagram showing the total duration of a sample of 52
films

(sorted)

As you can se from the above diagram

· the shortest film has duration of 77 mins, and the longest is 213
mins long

· most films are in the group 120-130 mins.

I have now decided to construct a frequency table so that I can draw a
cumulative frequency graph, which will enable me to draw a box and
whisker plot, and therefore visually see any or all outliers in my
data. Here follows my table:

Class

Frequency

Cumulative Frequency

70=
1

1

80=
4

5

90=
6

11

100=
9

20

110=
7

27

120=
12

39

130=
4

43

140=
2

45

150=
1

46

160=
3

49

170=
0

49

180=
2

51

190=
0

0

200=
0

0

210=
1

1

Total 52

See overleaf for cumulative frequency diagram.

From Graph:

First Quartile - 129 mins

Mean - 117 mins

Third Quartile - 103 mins

From my sorted stem and leaf diagram it is possible to calculate
median, first and third quartiles of my data, and so will now do so,
so that I can compare these results to those obtained from my graph.

First Quartile = ¼ x 52 + ½ = position 13.5

Value = 103 mins

Median = ½ x 52 + ½ = position 26.5

Value = 117 mins

Third Quartile = ¾ x 52 + ½ = position 39.5

Value = 129 mins

As you can see, my graph values deviate from the calculated values.
Therefore as the calculations will probably be more accurate than the
graph results, when I draw my box and whisker plot, I will use the
calculated values.

See below for box and whisker plot:

I am now going to calculate the mean and standard deviation of my data
so that I can see where the outliers of my data, if any, are.

Mean
====

Standard Deviation
------------------

In most data sets

· about 2/3 of the values lie within 1 standard deviation of the mean

· about 95% of the values lie within 2 standard deviations of the mean

· about 99.5% lies within 3 standard deviations.

To see if this is so with my data, I will now perform the relevant
calculations:

Mean = 120.13

120.13 + 27.91 = 148.04

120.13 - 27.91 = 92.22

Therefore about 2/3 of my data should lie between 92 mins and 148
mins. That is, about 34 values should be within this range. About 38
values are in this range, so this piece of information is relevant for
my information.

Mean = 120.13

120.13 + 2(27.91) = 175.95

120.13 - 2(27.91) = 64.31

Therefore about 95% of my data should lie in the range of 64 mins to
178 mins. About 49 values should be in this range. About 49 values are
in this range, and so I have identified that the outliers in my data
are 181, 186 and 213 mins.

SUMMARY OF WHAT I FOUND AND ACCURACY
====================================

I began this investigation with the aim of finding out the average
time of a song and determining how long or short a song can be without
the audience being bored or not pleased, respectively.

I found that the average duration of the sample of songs that I used
was about 235seconds. The shortest film in my sample was 125.4 seconds
long, and the longest was 325.2 seconds. About 2/3 of the sample of
films fell between 182.seconds and 284. seconds . Therefore my media
studies coursework should aim to be between about 182 seconds long and
about 284seconds long. I will aim to make the song to be about
233secondslong in total length, as this is the average between these
two values. I think that this investigation has been a success because
I have achieved what I set out to achieve: what length my song should
be for maximum audience enjoyment.

In terms of accuracy, I think that this investigation has been a
success. I have constructed a table to show my graph values, where
applicable, my previously calculated values and the computer's values:

Graph Value

My calculated value

Computer value

Mean

233.5

236.004

Standard Deviation

51.08

55.85029

Median

258

mode

202.2

As you can see, the only real discrepancy occurs with the computer's
standard deviation, and I can only conclude that this is because it
has used a mean with more decimal places, and therefore it is more
accurate. It also occurred because the calculated standard deviation
was found from grouped data and therefore only an estimate. Graph
discrepancies occur because of inaccurate drawing techniques. Other
than that, my values are, on the whole, pretty accurate.

The quality of the investigation could be improved by using a more
varied population, in an ideal world this would be an Internet site of
every film ever made. As this does not exist, the site that contains
the most comprehensive list of films will have to do. Which in this
case is the site that I used, the HMV superstore site. My method of
collection would not vary even if I used another site. If I used three
randomly picked numbers for each category, then I would end up with a
sample of 78 films, which I think is too produce an accurate report
on.

I think that this investigation was a success, as it helped me to gain
some information that will help me in another topic, and because it
was completed as accurately as I could.