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Q.1. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11 . The last two numbers are 10.

Find the mean of the $32$ numbers, such that if the mean of $10$ of them is $15$ and the mean of $20$ of them is $11$ . The last two numbers are $10$ .

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Write and solve direct variation equations

Full solution

Q. Find the mean of the

32

numbers, such that if the mean of

10

of them is

15

and the mean of

20

of them is

11

. The last two numbers are

10

.

Calculate Mean Total: Calculate the total sum of the first $10$ numbers using their mean. $\newline$ The mean of $10$ numbers is $15$ , so the total sum of these $10$ numbers is $10 \times 15$ . $\newline$ Calculation: $10 \times 15 = 150$
Calculate Next $20$ Total: Calculate the total sum of the next $20$ numbers using their mean. $\newline$ The mean of $20$ numbers is $11$ , so the total sum of these $20$ numbers is $20 \times 11$ . $\newline$ Calculation: $20 \times 11 = 220$
Add Last Two Numbers: Add the last two numbers to the total sum. $\newline$ The last two numbers are both $10$ , so their total sum is $10 + 10$ . $\newline$ Calculation: $10 + 10 = 20$
Calculate Combined Total: Calculate the combined total sum of all $32$ numbers. $\newline$ Add the sums from Step $1$ , Step $2$ , and Step $3$ . $\newline$ Calculation: $150 + 220 + 20 = 390$
Calculate Overall Mean: Calculate the mean of all $32$ numbers. $\newline$ Divide the combined total sum by the number of numbers, which is $32$ . $\newline$ Calculation: $390 / 32$
Perform Division: Perform the division to find the mean. $\newline$ Calculation: $390 / 32 = 12.1875$

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