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The mean and standard deviation of six observation are 8 and 4

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The mean and standard deviation of six observation are $8$ and $4$ respectively. If each observation is multiplied by $3$ , find the new mean and new standard deviation of the resulting observations.

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The mean and standard deviation of six observation are

8

and

4

respectively. If each observation is multiplied by

3

, find the new mean and new standard deviation of the resulting observations.

9 mins ago

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Text solutionVerified

If the mean and standard deviation of observations

x_{1}, x_{2} ..., x_{n}

are

\overline{X}

and

σ

respectively, then the mean and standard deviations of

a x_{1}, a x_{2} ..., a x_{n}

are

a \overline{X}

and

∣ a ∣ σ

respectively.

∴

New mean

= 8 \times 3 = 24

and, New standard deviation

= 3 \times 4 = 12.

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Question Text	The mean and standard deviation of six observation are $8$ and $4$ respectively. If each observation is multiplied by $3$ , find the new mean and new standard deviation of the resulting observations.
Answer Type	Text solution:1
Upvotes	152