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The average of 26 numbers is 54.5. The average of the first 15 numbers is 58.6 and that of the last 12 numbers is 52. What will be the average of the number if thr 15th number is excluded?

Question

The average of 26 numbers is 54.5. The average of the first 15 numbers is 58.6 and that of the last 12 numbers is 52. What will be the average of the number if thr 15th number is excluded?

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Solution

To solve this problem, we first need to find the sum of all 26 numbers, the sum of the first 15 numbers, and the sum of the last 12 numbers.

  1. The sum of all 26 numbers is 26 * 54.5 = 1417.
  2. The sum of the first 15 numbers is 15 * 58.6 = 879.
  3. The sum of the last 12 numbers is 12 * 52 = 624.

Next, we need to find the 15th number, which is included in both the first 15 numbers and the last 12 numbers. To do this, we subtract the sum of the last 12 numbers from the sum of the first 15 numbers: 879 - 624 = 255.

Now, to find the average of the numbers excluding the 15th number, we subtract the 15th number from the sum of all 26 numbers and divide by 25 (since we are excluding one number): (1417 - 255) / 25 = 46.48.

So, the average of the numbers excluding the 15th number is 46.48.

This problem has been solved

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