# The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be :

a. 50.5

b. 51

c. 51.5

d. 52

**Solution:**

It is given that

Mean of 100 observations is 50

n = 100

x̄ = 100

\(Mean=\frac{\sum_{i=1}^{n}x_{i}}{n} \)

\(\\\frac{1}{100}\times \sum_{i=1}^{100}x_{i}=50\\\sum_{i=1}^{100}x_{i}=5000\) …. (1)

Observation 50 is replaced by 150

Equation (1) will be

\(\sum_{i=1}^{100}x_{i}=5000 - 50 + 150=5100\)

\(Resulting\: mean=\frac{\sum_{i=1}^{100}x_{i}}{100}=\frac{5100}{100}=51\)

Therefore, the resulting mean will be 51.

**✦ Try This: **The mean of 200 observations is 100. If one of the observations which was 100 is replaced by 300, the resulting mean will be :

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 14

**NCERT Exemplar Class 9 Maths Exercise 14.1 Problem 18**

## The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be : a. 50.5, b. 51, c. 51.5, d. 52

**Summary:**

The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be 51

**☛ Related Questions:**

- There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is f . . . .
- The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is . . . .
- The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is a. 45, b. 49.5, c. 54, d. 56

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