Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are foot lengths in inches of randomly selected women in a study of a country's military in 1988. Are the statistics representative of the current population of all women in that country's military?

10.2 8.7 9.9 8.7 9.5 10.4 8.6 9.0 9.1 99 9.9

mean = 9.5

median = 9.5

mode = 9.9

mid-range = 9.5

Step-by-step explanation:

Using the population as 10.2 8.7 9.9 8.7 9.5 10.4 8.6 9.0 9.1 99 9.9

(a) mean is the average of all numbers

hence

mean = (10.2 + 8.7 + 9.9 + 8.7 + 9.5 + 10.4 + 8.6 + 9.0 + 9.1 + 9.9 + 9.9) / 11

= 103.9/11

= 9.5

(b) Median is the middle value for rearranged population data

For the median, there is need to rearrange population data

this generates 8.6, 8.7, 8.7, 9.0, 9.1, 9.5, 9.9, 9.9, 9.9, 10.2, 10.4

since n = 11, the median is (n+1) / 2 th value = (11+1) / 2 = 6th value

median = 9.5

(c) mode is the highest occurring value. from the rearranged data

8.6, 8.7, 8.7, 9.0, 9.1, 9.5, 9.9, 9.9, 9.9, 10.2, 10.4,

9.9 occurs three times hence the mode

(d) mid-range is mathematically the average of the lowest and highest values

hence mid-range = (8.6 + 10.4) / 2

= 19/2

= 9.5

(e) The statistics is not totally representative of the current population of all women in the country's military even though the mean, median and mid range all gave similar values of 9.5; this implies that is 9.5 inches is used for the foot size of the women in the military, there will be substantial consideration.

The mode which has the frequency for highest considered number of women military shows a value of 9.9 which wont be able to use the size of 9.5 inches generated from the other estimates.

The problem of mean, mode, median and mid-range is that it is at best only estimates; it tries to refer back to an acceptable middle value without considering the span of the population hence it is not a good statistic to represent the population.

This is exemplified in the given population where only one woman has a foot size of 9.5 inches. Others wont be able to use the estimated statistics