Question

Best Measure of Center

Juan's Homeruns

Season Number of Homeruns
1 0
2 18
3 23
4 25
5 28
6 30
7 31
8 33
9 55
Question 1

The table shows the number of homeruns that Juan scored during his last nine seasons in professional baseball. Which values, if any, are outliers for the data set?
Responses

A 00

B 18 and 3318 and 33

C 0 and 550 and 55

D no outliersno outliers
Question 2

Which statement is TRUE about the best measure of center to use when describing the data set?
Responses

A The mode is the best measure to use because no value is repeated.The mode is the best measure to use because no value is repeated.

B The range is the best measure to use because the data has outliers.The range is the best measure to use because the data has outliers.

C The median is the best measure of center to use because the data has outliers.The median is the best measure of center to use because the data has outliers.

D The mean is the best measure of center to use because it tells the average number of homeruns.

Answer 1

Question 1 — Outliers
Compute quartiles: sorted data = 0, 18, 23, 25, 28, 30, 31, 33, 55
Median = 28 (5th value). Q1 = median of lower half = (18+23)/2 = 20.5. Q3 = median of upper half = (31+33)/2 = 32.
IQR = 32 − 20.5 = 11.5.
Lower fence = 20.5 − 1.5(11.5) = 3.25. Upper fence = 32 + 1.5(11.5) = 49.25.
Values outside (below 3.25 or above 49.25) are outliers: 0 and 55.
Answer: C (0 and 55).

Question 2 — Best measure of center
Because the data set has outliers (0 and 55) the median is the best measure of center (it is not pulled by outliers).
Answer: C.