# NCERT Class 11 Mathematics Solutions: Chapter 15 – Statics Miscellaneous Exercise Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. The mean and standard deviation of six observations are , respectively. If each observation is multiplied by , find the new mean and new standard deviation of the resulting observations.

Consider the observations be .

It is given that mean is and standard deviation is .

Mean, … eq (1)

If each observation is multiplied by and the resulting observations are , then

For

New Mean,

… [Using (1) ]

Standard deviation,

… eq (2)

From eq (1) and (2)

It can be observed that,

Substituting the values of and in eq (2)

So, variance of new observations

The standard deviation of new observations is

2. Given that is the mean and is the variance of n observations . Prove that the mean and variance of the observations are and , respectively .

The given n observations are .

Mean

Variance

… eq (1)

If each observation is multiplied by and the new observations are , then

So, mean of the observations, , is

Substituting the values of in (1)

The variance of the observations, .

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