With what value should the highest quantity in the data : 65, 52, 14, 26, 18,…
2024
With what value should the highest quantity in the data : 65, 52, 14, 26, 18, 35, 32, 38 be replaced so that the mean and median become equal?
- A.
79
- B.
63
- C.
53
- D.
50
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Show answer & explanation
Correct answer: C
Sort the data: 14, 18, 26, 32, 35, 38, 52, 65
Median = (32 + 35) / 2 = 33.5
Let x be the value replacing the highest quantity (65). The original total sum is 280, so the new sum is 280 - 65 + x = 215 + x.
For mean to equal median: (215 + x) / 8 = 33.5
Solve: 215 + x = 33.5 × 8 = 268, so x = 268 - 215 = 53.
Check: Replacing 65 with 53 yields the list 14, 18, 26, 32, 35, 38, 52, 53. The middle two remain 32 and 35 (median 33.5) and the mean is (215 + 53)/8 = 268/8 = 33.5, so mean and median are equal.
Answer: 53