The mean of 22 numbers is 14.What is the new mean if each number is increased by 4
Answers
Answer:
Step-by-step explanation:
Mean =14
No of terms=22
So 14=sum of observation/22
Sum of observation =308
No to be added=4×22=88
New mean =308+88/22
New mean =18
Answer:
18
Step-by-step explanation:
Let the numbers be x1, x2, x3, ..... , x22.
Hence, as given,
(x1 + x2 +x3 + ..... + x22) ÷ 22 = 14 ----- eq. 1
When the numbers are increased by 4, they become
x1 + 4, x2 + 4, x3 + 4, ..... , x22 + 4.
Mean of these numbers:
{(x1 + 4) + (x2 + 4) + (x3 + 4) + .... + (x22 + 4)} ÷ 22
= {(22 × 4) + (x1 + x2 + x3 + ..... + x22)}
÷ 22
= {(22 × 4) ÷ 22 + (x1 + x2 + x3 + ... +
x22) ÷ 22}
= {4 + 14} ---- from eq.1
= 18
P. S. One short cut you can use in such questions is that when a particular number is added to all the observations, the same number added to the original mean gives the new mean.
Similarly, when a number is multiplied to all observations, it is multiplied to the mean.
The same goes when a number is subtracted from all the observations or when all observations are divided by a number, i.e. the same operation is performed to the mean with the same number.