Question

compare each set of data. determine which set shows greater variability.
set a
5, 8, 9, 10, 12, 15, 16, 20
set b
24, 34, 37, 42, 56, 57, 65
which set shows greater variability?
which measure provides greater variability for the set you chose?
range
interquartile range
both range and interquartile range

Explanation:

Step1: Calculate range of Set A

Range = Maximum - Minimum. For Set A, maximum = 20, minimum = 5. So range of Set A = 20 - 5=15.

Step2: Calculate range of Set B

For Set B, maximum = 65, minimum = 24. So range of Set B = 65 - 24 = 41.

Step3: Calculate median of Set A

Arrange Set A in ascending - order: 5, 8, 9, 10, 12, 15, 16, 20. There are 8 numbers. Median is the average of the 4th and 5th numbers. Median = $\frac{10 + 12}{2}=11$.
Lower half: 5, 8, 9, 10. Q1 (first - quartile) is the median of the lower half. Since there are 4 numbers in the lower half, Q1=$\frac{8 + 9}{2}=8.5$. Upper half: 12, 15, 16, 20. Q3 (third - quartile) is the median of the upper half. Since there are 4 numbers in the upper half, Q3=$\frac{15+16}{2}=15.5$. Inter - quartile range of Set A (IQR) = Q3 - Q1 = 15.5 - 8.5 = 7.

Step4: Calculate median of Set B

Arrange Set B in ascending - order: 24, 34, 37, 42, 56, 57, 65. There are 7 numbers. Median is the 4th number, so median = 42.
Lower half: 24, 34, 37. Q1 is the median of the lower half, so Q1 = 34. Upper half: 56, 57, 65. Q3 is the median of the upper half, so Q3 = 57. Inter - quartile range of Set B (IQR) = Q3 - Q1 = 57 - 34 = 23.

Step5: Compare variability

Since the range of Set B (41) > range of Set A (15) and the inter - quartile range of Set B (23) > inter - quartile range of Set A (7), Set B shows greater variability. And both range and inter - quartile range provide greater variability for Set B.

Answer:

Set B
Both range and interquartile range