Question

A survey asked 11 people to report the amount of money they spend eating out for lunch on a day. Men Women 19 a) Compare the median amount of money men spend on lunch to that for the women. The median money that men spend was $ and the median for the women was S showing that the typical Select an answer tended to spend more money for lunch. b) Compare the interquartile range for the men to that for the women. The interquartile range for the men was and the interquartile range for the women was showing more variation in the amount of money spent on lunch for Select an answer

Answer 1

Solution:
Let's sort the data for male and female from the smallest to largest data value as follows:

Men	Women
13	10
13	10
15	10
15	10
16	10
17	11
17	11
19	13
19	14
19	14
20	15

Solution(a)
n=11
Median can be calculated as
Median = (n+1)/2 = (11+1)/2 = 6th values
So Median for Men = 17
Median fro women = 11
The median money that men spend was 17$ and the median for the women was 11$ showing that the typical Men tended to spend more money on lunch.
Solution(b)
The interquartile range can be calculated as
Interquartile range = Q3 - Q1
Q1 = (n+1)/4 = (11+1)/4 = 3rd value
Q3 = 3*(n+1)/4 = 3*(11+1)/4 = 9th value
So Q1 and Q3 for men is 15 and 19 so interquartile range for men = 19-15 = 4
Q1 and Q3 for women is 10 and 14 so interquartile range for men = 14-10 = 4
Range for Men = 20 - 13 = 7
Range for Women = 15 - 10 = 5
The interquartile range for the men was 4 and the interquartile range for the women was 4 showing both are the same but the range for men is more so more variation in the amount of money spent on lunch for men.