Table of Contents

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Variance and standard deviation

People use both, but for different things.As Jacob Joseph wrote, standard deviation is in the same units as the mean, so it can be used with the mean to set confidence intervals.

,Suppose I measured the height of 100 people and got a mean of 1.

7 meters and a standard deviation of 0.

2 meters.

That gives you some idea of the distribution of heights.

But if I told you the variance was 0.

04 square meters, thereu2019s not much you can do with that information (except take the square root to get the standard deviation).

,But now suppose I told you that sex explained 0.

01 variance.

Taking the square root to get 0.

1 standard deviation doesnu2019t tell you anything.

But taking 0.

01 and dividing it by the 0.

04 variance tells you sex explains 25% of the variance in height.

The sum of all independent explanatory factors is 100%, so you know how much sex tells you about height, and how much is due to other factors.

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How to find the standard deviation

IF the values of Mean Median and Mode are equal and empirical relation is satisfied and Skeweness is O and kurtosis is 0 then the Distribtutiin of the data is called Normal distribution,The graph of the Normal distribution data is a bell shaped curve and drawn using centre ( Mean=Median =Mode) and points on X axis Horizontal line at a distance of Standard deviation from the Mean Mean+--1sd mean+--2sd and mean+-3sd representing 68% 95%99% of cases respectively of the population,Calculation of standard deviation using step Deviation method,Class f Mid X d (X-A)/I d^2 fd fd^2,0-50 15 25 - -2 4 -30 60,50-100 20 75 -1 1 -20 20,100 -150 18 125 0 0 0 0,150-200 25 175 +1 1 25 25,200-250 22 225 +2 4 44 88,Totals sigma f =100,Sigma fd =19,Sigma fd^2=193,Assumed Arithmetic Mean is 125,Mean =A0+sigma fd/ sigma f,=125+19/100 u00d750=125+9.5=134.

50,Mean of the distribution is 134 .

50,Standard deviation is calculated using the formula,Sd =[(sigma fd^2 /sigma f )--(sigma fd^2/ sigma f)]^1/2,Writing the values,Standard deviation is =[193/100 -(19/100)^2]^1/2,=68.

5,Standard deviation of the frequency distribution is 68.

5,51% of The scores of the data are spread from the Mean of the data,Coefficient of Variance =Standard deviation/Mean u00d7100= (68.

6/134.

5 )u00d7100 = 50.

93 =51%,For further information and practice refer,Your class Text Books,NCEERT Mathematics class Text Books,Refer statistics.

Com

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Variance and standard deviation example

The central tendency mean gives you the idea of average of the data points( i.e centre location of the distribution),And now you want to know how far are your data points from mean,So, here comes the concept of variance to calculate how far are your data points from mean ( in simple terms, it is to calculate the variation of your data points from mean),Population variance : sumlimits_{i=1}^n frac{(x_i-mu)^2}{N}Sample variance : sumlimits_{i=1}^n frac{(x_i-overline{x})^2}{n-1}Standard deviation is simply the square root of variance .

And standard deviation is also used to calculate the variation of your data points,(And you may be asking, why do we use standard deviation , when we have variance.

Because, in order to maintain the calculations in same units i.

e suppose mean is in cm/m, then variance is in cm^2/m^2 , whereas standard deviation is in cm/m , so we use standard deviation most)

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Variance and standard deviation questions and answers

This is binomial.VAR = NPQ, N=3, P=.

90, Q=.

10.

So VAR.

= .

27.

STD DEV.

= SQRT(.

27) = .

5196+.