Question

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?

Answer 1

Given:The given data is (in inches)

9.6, 9.8, 10.2, 9.8, 9.7, 8.9, 10.3, 9.9, 9.3, 10.2, 10.2.

Required:

(a) Mean

(b) Median

(c) Mode

(d) Mid-Range

Step-by-step explanation:

Let us first arrange the data in ascending order

8.9, 9.3, 9.6, 9.7, 9.8, 9.8, 9.9, 10.2, 10.2, 10.2, 10.3

(a) Mean

The mean of data is sum of observations divided by number of observations

`\begin{gathered} Mean=(8.9+9.3+9.6+9.7+9.8+9.8+9.9+10.2+10.2+10.2+10.3)/(11) \\ Mean=9.809 \end{gathered}`

(b) Median

Since there are 11 terms, so median is

`(11+1)/(2)=(12)/(2)=6th\text{ term}`

So median is

`Median\text{ = }9.8`

(c) Mode

Mode is most occured frequency

so here 10.2 occurs most of the time (3 times)

`Mode=10.2`

(d) Mid range

Mid range is average of least and highest frequency

`Mid\text{ range = }(8.9+10.3)/(2)=9.2`

Final Answer:

(a) Mean = 9.809

(b) Median = 9.8

(c) Mode = 10.2

(d) Mid range = 9.2