# The mean and standard deviation of a group of 100 observations were found to be 20 and 3 , respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted

**Solution:**

Number of observations = 100

Incorrect mean (x) = 20

Incorrect standard deviation (σ) = 3

20 = 1/100 ∑^{100}_{i = 1}x_{i}

∑^{20}_{i = 1}x_{i}= 20 × 100

= 2000

That is, incorrect sum of observations

= 2000

Correct sum of observations

= 2000 - 21 - 21 - 18

= 2000 - 60

= 1940

Therefore,

correct mean = correct sum/(100 - 3) = 1940/97 = 20

Standard deviation,

σ = √ 1 / N ∑N_{i} = 1 (X_{i}^{2} − μ^{2})

3 = √ 1 / 100 ∑N_{i} = 1 (X_{i}^{2} − μ^{2})

= Incorrect ∑^{n}_{i = 1} x_{i}² = 100 (9 + 400)

= 40900

Correct ∑^{n}_{i = 1} x_{i}² = 4

= Incorrect ∑^{n}_{i = 1} x_{i}² - (21)² - (21)² - (18)²

= 40900 - 441 - 441 - 324

= 39694

Correct standard deviation

= √39694/97 - (20)²

= √409.216 - 400

= √9.216

= 3.036

NCERT Solutions Class 11 Maths Chapter 15 Exercise ME Question 7

## The mean and standard deviation of a group of 100 observations were found to be 20 and 3 , respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

**Summary:**

Given that the mean and standard deviation of a group of 100 observations were found to be 20 and 3. Correct mean and correct standard deviation are 20 and 3.036

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