Question

Josh and Richard each earn tips at their part-time jobs. This table shows their earnings from tips for five days.

Question:

a) Who had the greater median earnings from tips? You must show your work to receive credit.
b) What is the difference in the median of Josh's earnings from tips and the median of Richard's earnings from tips? You must show your work to receive credit.
c) What is the difference in the interquartile range for Josh's earnings from tips and the interquartile range for Richard's earnings from tips? You must show your work to receive credit.

Answer 1

a) Richard had the greater median earnings from tips

b) $10

c) $1

Explanation:

Median is the middle number when arranged from least to greatest.

a)

Josh's Tips (smallest to greatest): 20, 28, 31, 36, 40

Richard's Tips (smallest to greatest): 28, 40, 41, 45, 53

The middle number (median) for Josh is the 3rd number, which is 31

The middle number (median) for Richard is the 3rd number, which is 41

Richard had the greater median earnings from tips

b)

Josh's median is 31 and Richard's median is 41. The difference is:

41 - 31 = $10

c)

Interquartile range is Third Quartile - First Quartile

For 5 number series, the third quartile is the average of 4th and 5th number. The first quartile is the average of the 1st and 2nd number.

For Josh:

Average of 4th and 5th number: (36+40)/2 = 38

Average of 1st and 2nd number: (20+28)/2 = 24

Interquartile Range = 38 - 24 = 14

For richard:

Average of 4th and 5th number: (45+53)/2 = 49

Average of 1st and 2nd number: (28+40)/2 = 34

Interquartile Range = 49 - 34 = 15

Thus, difference in IQR (interquartile range) between Josh and Richard is 15 - 14 = 1