Question

HELPPPPPPPPPPP

1. Shown are the final scores for Norm Duke in the past eight bowling tournaments.
299, 281, 285, 269, 280, 269, 286, 287

Part A: What is the mean absolute deviation of Norm Duke’s scores?

A.
7.50

B.
7.00

C.
7.25

D.
6.75

Part B: Based on the mean absolute deviation from Part A, who has been the more consistent bowler if Ryan Shafer has a mean absolute deviation of 7?

A.
Norm Duke has been more consistent because his mean absolute deviation is greater than Ryan Shafer’s.

B.
Ryan Shafer has been more consistent because his mean absolute deviation is less than Norm Duke’s.

C.
Ryan Shafer has been more consistent because his mean absolute deviation is greater than Norm Duke’s.

D.
Norm Duke has been more consistent because his mean absolute deviation is less than Ryan Shafer’s.

Answer 1

Part A

• C. 7.25

Part B

• B. Ryan Shafer has been more consistent because his mean absolute deviation is less than Norm Duke’s.

Explanation:

Given data:

• 299, 281, 285, 269, 280, 269, 286, 287

Part A

Find the mean of the data above:

• (299 + 281 + 285 + 269 + 280 + 269 + 286 + 287)/8 = 282

Find absolute deviations, an absolute value of the difference of data and the mean:

• 299 - 282 = 17 ⇒ 17
• 281 - 282 = -1 ⇒ 1
• 285 - 282 = 3 ⇒ 3
• 269 - 282 = -13 ⇒ 13
• 280 - 282 = 2 ⇒ 2
• 269 - 282 = -13 ⇒ 13
• 286 - 282 = 4 ⇒ 4
• 287 - 282 = 5 ⇒ 5

Find mean absolute deviation:

• (17 + 1 + 3 + 13 + 2 + 13 + 4 + 5)/8 = 7.25

Correct choice is C

Part B

Less mean absolute deviation is the sign of more consistent data.

Since Ryan Shafer has smaller mean absolute deviation, he has been more consistent 7 < 7.25

Correct choice is B.