Question

The mean of a set of 10 number is M . By combining with it a second set of M numbers, the mean of the combined set becomes 10. What is the sum of the second set of numbers ?​

Answer 1

Answer:

100

Step-by-step explanation:

10M+MX /10+M = 10

10M + MX = 100 + 10M

10M + MX - 10M = 100

MX = 100

X= 100/M

sum of second number is MX

M×100/M =100

Answer 2

Concept:

Apart from the mode and median, the mean is one of the measures of central tendency used in statistics. The average of a group of values is known as the mean. It refers to a data set's values being distributed evenly.

Given:

The mean of the first set $=M.$

The mean of the second set $=10.$

Find:

What is the sum of the second set of numbers?

Solution:

The mean is calculated by dividing the sum of the provided numbers by the total number of numbers.

Mean = (Sum of all the observations ÷ Total number of observations)

The mean of the first set $=M$

Total number of observations of the first set $=10$

Let the sum of the first set be Sum1.

$Mean1=\frac{Sum1}{10}$

$M=\frac{Sum1}{10}$                            ...... eq(1)

( ∵$Mean=M$)

Let the sum of the second set be Sum2.

Total mean of both sets $=10$

Total number of observations of the second set $=M$

Total number of observations of both the sets $=M+10$

Total mean $=\frac{Sum1+Sum2}{10+M}$

$\frac{Sum1+Sum2}{10+M}=10$

( ∵ Total mean$=10$)

$Sum1+Sum2=10(10+M)$

$Sum1+Sum2=100+10M$

Put the value of M from eq (1)

$Sum1+Sum2=100+10(\frac{Sum1}{10} )$

$Sum1+Sum2=100+Sum1\\Sum2=100$

Hence the sum of the second set of numbers is $100.$