Question

1. jack and his twin brother bill kept track of how much they earned mowing yards during the summer weeks. their earnings are listed on the chart below. jack and bills summer earnings week jacks earnings bills earnings 1 $18 $12 2 $32 $16 3 $16 $32 4 $18 $16 5 $32 $32 6 $32 $50 7 $32 $50 8 $32 $75 9 $16 $48 which statement below is true about this data? a. jacks earnings have a greater range than bills earnings. b. jacks earnings show a greater variability than bills earnings. c. bills earnings have a greater range than jacks earnings. d. bills earnings have a greater median than jacks earnings.

Explanation:

Step1: Find Jack's range

Range = Max - Min. Jack's max = 32, min = 16. Range = 32 - 16 = 16.

Step2: Find Bill's range

Bill's max = 75, min = 12. Range = 75 - 12 = 63.

Step3: Analyze option A

Since 16 (Jack's range) < 63 (Bill's range), option A is false.

Step4: Analyze option B

Just by looking at the ranges, Bill's data has more spread (greater range), so Jack does not have greater variability. Option B is false.

Step5: Analyze option C

As calculated, Bill's range (63) > Jack's range (16), so option C is true.

Step6: Find Jack's median

Arrange Jack's earnings: 16, 16, 16, 18, 18, 32, 32, 32, 32. Median (9 values, middle is 5th value) = 18.

Step7: Find Bill's median

Arrange Bill's earnings: 12, 16, 16, 16, 32, 32, 48, 50, 75. Median (9 values, middle is 5th value) = 32. But we already know C is true from range - check for completeness. Since 18 (Jack's median) < 32 (Bill's median), option D is also true. But range - based answer is more straightforward for this data - comparison problem.

Answer:

C. Bill's earnings have a greater range than Jack's earnings.