Question

Standard Deviation (S.D) for two observations 1 and 4 is​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Observations are 1 and 4}$

$\underline{\textsf{To find:}}$

$\textsf{Standard deviation of given two observations}$

$\underline{\textsf{Solution:}}$

$\textsf{First we find out mean of given two observations}$

$\mathsf{Mean,\bar{x}=\dfrac{1+4}{2}=\dfrac{5}{2}}$

$\mathsf{Formula\;for\;Standard\;deviation:}$

$\boxed{\mathsf{S.D=\sqrt{\dfrac{\sum\,(x_i-\bar{x})^2}{n}}}}$

$\mathsf{S.D=\sqrt{\dfrac{(x_1-\bar{x})^2+(x_1-\bar{x})^2}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{(1-\frac{5}{2})^2+(4-\frac{5}{2})^2}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{(\frac{2-5}{2})^2+(\frac{8-5}{2})^2}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{(\frac{-3}{2})^2+(\frac{3}{2})^2}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{\frac{9}{4}+\frac{9}{4}}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{\frac{18}{4}}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{\frac{9}{2}}{2}}}$

$\mathsf{S.D=\sqrt{\dfrac{9}{4}}}$

$\mathsf{S.D=\dfrac{3}{2}}$

$\therefore\boxed{\mathsf{Standard\;devation=1.5}}$

$\underline{\textsf{Find more:}}$

If the variance of 1,2,3,4......

..,10 is 99/12 , then S.D. of 3,6,9,12 ......,30 is

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If standard deviation of the values 2, 4, 6, 8 is 2.236, then standard deviation of the values 4, 8, 12, 16 is​

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the standard deviation of 20 observations is root 5.if each observation is multiplied by 2. find the standard deviation and variance of the resulting observation.​

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Answer 2

Answer:1.5

Step-by-step explanation: