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Conclusion

8.3.12.4 Averages The 'average' for a variable is a single figure that is representative of all the values of the variable. It is some sort of 'middle' figure. More accurately, 'averages' are known as measures of central tendency.

It is possible to compute the average age of consent that the sample thinks appropriate for gays.

Sometimes data is best summarised as an average, especially for comparison purposes. For example, one might compute the average age of consent for males (V22, see Table 8.3.12.3) and compare it with the average for females (V21).

Computation of averages can be done by hand or by computer. The important thing is not working out the average but knowing what it means.

There are several different measures of central tendency: including mode, median and arithmetic mean.

8.3.12.4.1 Mode
The simplest measure of central tendency is the mode. This is the value of a variable that occurs most often. From Table 8.3.12.3 we can see that '18 years old' is the age that more people choose than any other. Thus the mode is '18 years old'. (The 40 people whose answer is missing are excluded and we have a sample of 111.)

8.3.12.4.2 Median
The median is the value that lies in the middle of the distribution when all the values are put in rank order. The easiest way to locate the median is to look down the cumulative percentage column (when available) and locate which value corresponds to 50% (half way).

In Table 8.3.12.3, 29.7% of the sample think the age should be 17 or less and 59.5% think it should be 18 or less. So the middle (that is, 50%) value will be 18. (It would be possible to estimate what the exact value would be in years and months assuming that the 18-year olds are spread evenly throughout the year, but this is unnecessary in this case).

8.3.12.4.3 Arithmetic mean
The arithmetic mean (which is often called 'the' average) is the total of all the values of a variable divided by the number in the sample. There are 112 values for V21 so we need to compute the total of the 112 ages. Table 8.3.12.5 shows how to calculate the mean without the aid of a computer program. The result in this case is an arithmetic mean of 22.125 years.

Table 8.3.12.5 Calculation of the mean age for V22: What should the consent age be for men?

Value
x

Frequency
f

Frequency x value
fx

12

1

12

14

2

28

15

1

15

16

28

448

17

2

34

18

33

594

19

1

19

20

8

160

21

26

546

25

2

50

30

2

60

60

1

60

78

1

78

80

1

80

98

3

294

Total

n=112

Total fx=2478

Arithmetic mean = Total fx dived by sample size (n)
Arithmetic mean = 2478/112 = 22.125

Note: the greek letter sigma '∑', is used as a shorthand for 'Total' , so the formula for the Arithmetic mean calclated from a frequency table is: Arithmetic mean = ∑fx/n

The arithmetic mean gives a much larger value of the average in this case than either the mode or the median. Which average is the best? The answer to that depends in the first instance on the level of measurement or scale of the data. This relates to the type of data that is being 'averaged'. Broadly speaking, social research data is either nominal, ordinal, interval or ratio.