Question

7. For a set of 10 observations, the mean was calculated and was found to be 15. It was later

found, on scrutiny, that the last observation of the set should have 20 instead of 10. Calculate

the correct mean.​

Answer 1

Answer :

The correct mean = 16

Step-by-step explanation :

$\underline{\bf Mean:}$

⇒ It is the average of the numbers.

⇒ Add up all the terms and divide the number of terms in the data set.

⇒ The mean of x₁, x₂, x₃ ,..., xₙ

     $\bf Mean=\frac{x_1+x_2+x_3+...+x_n}{n}$

⇒ Mean = sum of observations/number of observations

________________________________

Given,

• For a set of 10 observations, the mean was calculated and was found to be 15
• the last observation of the set should have 20 instead of 10

At first,

one of the observations = 10

no.of observations = 10

Mean = 15

$\bf Mean=\frac{sum \ of \ observations}{no.of \ observations}}$

$15=\frac{Sum \ of \ 9 \ observations+10}{10} \\\\ \text{sum of 9 observations + 10} 15 \times 10 \\\\ \text{sum of 9 observations + 10} =150 \\\\ \text{sum of 9 observations} =150-10 \\\\ \text{sum of 9 observations}=140$

Later,

One of the observations = 20 (instead of 10)

no.of observations = 10

Correct mean = ?

$\bf Mean=\frac{sum \ of \ observations}{no.of \ observations}}$

$Correct \ mean=\frac{sum \ of \ 9 \ observations+20}{10} \\\\ \text{Correct mean} =\frac{140+20}{10} \\\\ \text{Correct mean} =\frac{160}{10} \\\\ \text{Correct mean}=16$

∴ Correct mean = 16