Question

the table below shows the bowling scores of 11 students from baruch middle school last wednesday.
bowling scores
40 64 66 67 67 68 69 70 71 72 78
part a
what is the range of this data - set?
part b
what is the interquartile range of this data - set?
part c
which measure, the range or the interquartile range, is a better measure of the spread of this data - set? why?

Explanation:

Step1: Arrange data in ascending order

40, 54, 66, 67, 67, 68, 69, 70, 71, 72, 78

Step2: Calculate the range (max - min)

Range = 78 - 40 = 38

Step3: Find the median

Since there are 11 data - points, the median is the 6th value. Median (Q2)=68

Step4: Find the lower half and upper half

Lower half: 40, 54, 66, 67, 67. Median of lower half (Q1)=66
Upper half: 69, 70, 71, 72, 78. Median of upper half (Q3)=71

Step5: Calculate the inter - quartile range (IQR = Q3 - Q1)

IQR = 71 - 66 = 5

Step6: Analyze the better measure of spread

The inter - quartile range is a better measure of spread because the value 40 is an outlier. The range is affected by outliers, while the inter - quartile range is resistant to outliers.

Answer:

Part A: 38
Part B: 5
Part C: The inter - quartile range is a better measure of the spread of this data set because the value 40 is an outlier. The range is affected by outliers, while the inter - quartile range is resistant to outliers.