# The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted?

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NDA (Held On: 23 April 2017) Maths Previous Year paper
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1. 18
2. 20
3. 21
4. 22

Option 2 : 20
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Electric charges and coulomb's law (Basic)
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## Detailed Solution

Concept:

Mean: It is the average of given observation. Let x1, x2, …, xn be n observations, then

Mean $$= {\rm{\bar X}} = \frac{{\mathop \sum \nolimits_{{\rm{i}} = 1}^{\rm{n}} {{\rm{x}}_{\rm{i}}}}}{{\rm{n}}}$$

Calculation:

Given: Mean (X̅) = 20

Mean is given as, $$\frac{{{{\rm{x}}_1} + {{\rm{x}}_2} + \ldots + {{\rm{x}}_{\rm{n}}}}}{{\rm{n}}} = {\rm{\bar X}}$$

Sum of incorrect observations = n X̅

= 100 × 20

= 2000

Removing incorrect observations, sum of observations = 2000 – 21 – 21 – 18 – 20

= 1920

So, new mean $$= \frac{{1920}}{{96}}$$

= 20
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