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The average of first fourteen numbers in an order set of thirty numbers is 9 and average of last fourteen numbers in the set is 5.If the sixteen number is 7 and the average of the thirty number is?5678

Question

The average of first fourteen numbers in an order set of thirty numbers is 9 and average of last fourteen numbers in the set is 5.If the sixteen number is 7 and the average of the thirty number is?5678

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Solution 1

The question seems to be a bit confusing, but I'll try to interpret it as best as I can.

We know that the average of the first 14 numbers is 9 and the average of the last 14 numbers is 5. We also know that the 16th number is 7. We're asked to find the average of all 30 numbers.

First, let's find the total sum of the first 14 numbers and the last 14 numbers.

The sum of the first 14 numbers is 14 * 9 = 126. The sum of the last 14 numbers is 14 * 5 = 70.

Now, we know that the 16th number is 7. But we don't know the 15th and the 17th to 30th numbers. However, we do know that the 15th to 30th numbers (16 numbers in total) have an average of 5. So, their total sum is 16 * 5 = 80.

But we've already counted the 16th number (which is 7) and the last 14 numbers (which sum up to 70) in this total. So, the 15th number must be 80 - 70 - 7 = 3.

So, the total sum of all 30 numbers is 126 (sum of the first 14 numbers) + 3 (the 15th number) + 7 (the 16th number) + 70 (sum of the last 14 numbers) = 206.

Finally, the average of all 30 numbers is the total sum divided by the number of numbers, which is 206 / 30 = 6.87 (rounded to two decimal places).

This problem has been solved

Solution 2

The question seems to be a bit confusing, but I'll try to interpret it as best as I can.

The average of a set of numbers is calculated by adding all the numbers in the set and then dividing by the count of numbers.

  1. The average of the first 14 numbers is 9. So, the total of these 14 numbers is 14*9 = 126.
  2. The average of the last 14 numbers is 5. So, the total of these 14 numbers is 14*5 = 70.
  3. The 16th number is 7.

Now, if we add these up, we get the total of the 30 numbers: 126 + 70 + 7 = 203.

The average of these 30 numbers would then be the total divided by the count of numbers: 203/30 = 6.77 (rounded to two decimal places).

So, the average of the thirty numbers is approximately 6.77.

This problem has been solved

Solution 3

The question seems to be a bit confusing, but I'll try to interpret it as best as I can.

The average of a set of numbers is calculated by adding all the numbers in the set and dividing by the count of numbers.

  1. The average of the first 14 numbers is 9. So, the total of these 14 numbers is 14 * 9 = 126.
  2. The average of the last 14 numbers is 5. So, the total of these 14 numbers is 14 * 5 = 70.
  3. The 16th number is 7.

The total of all 30 numbers in the set is the sum of the above, which is 126 + 70 + 7 = 203.

Therefore, the average of all 30 numbers is the total divided by the count of numbers, which is 203 / 30 = 6.77 (rounded to two decimal places).

This problem has been solved

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