How does the average change if the minimum number is removed from the list below? Round your answer to the nearest hundreths.
24 36 10 56 12 6 41 28
A
Increase by 2.95
B
Decrease by 2.95
Increase by 0.75
D Decrease by 0.75
E
Decrease by 3.12

9514 1404 393

  A  Increase by 2.95

Step-by-step explanation:

Suppose the current average is A. Then the sum of the 8 items being averaged is 8A. We observe the minimum of those items is 6, so removing that from the sum gives 8A-6. The new average of the 7 remaining items is ...

  A' = (8A -6)/7

The difference between the new average and the old one is ...

  A' -A = (8A -6)/7 -A = (A -6)/7

The average of the given items is ...

  (24 +36 +10 +56 +12 +6 +41 +28)/8 = 26.625

so the change in the average will be ...

  (26.625 -6)/7 ≈ 2.9464 ≈ 2.95 . . . an increase

The removal of the minimum number from the average will increase it by about 2.95.

Additional comment

The average is always greater than the minimum item, so removing the minimum item from the list will always increase the average. The amount of increase depends on the relationship between the average and the minimum, as we calculated above.

step-by-step explan mxfcg'k; uafwgzfgjhklhgation:

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