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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

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