Question

Q. Find variance and S.D. for the following set
of numbers.

65, 77, 81, 98, 100, 80, 129​

Answer 1

Answer:want does SD means

Step-by-step explanation:

Answer 2

The variance is $s^2=443.33$ and standard deviation is s=21.05

Step-by-step explanation:

Given set of numbers are  65, 77, 81, 98, 100, 80, 129​

To find the variance and standard deviation :

First find the $\overline{X}$

$Mean=\frac{65+77+81+98+100+80+129​}{7}$

$=\frac{630}{7}$

$=90$

Therefore $Mean=\overline{X}=90$

x          $x-\overline{X}$                                $(x-\overline{X})^2$

_____________________________

65       65-90=-25                                  625

77        77-90=-13                                    169

81         81-90=-9                                       81

98        98-90=8                                       64

100       100-90=10                                  100

80         80-90=-10                                  100

129        129-90=39                                1521

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                                                      $\sum (x-\overline{X})^2=2660$

_________________________________________________

We know that the formula for variance is

$s^2=\frac{\sum (x-\overline{X})^2}{n-1}$

• Here n=7 and substitute the values in the formula we have that
• $s^2=\frac{2660}{7-1}$
• $s^2=\frac{2660}{6}$
• $=443.33$

Therefore variance is $s^2=443.33$

Now standard deviation is

$s=\sqrt{\frac{\sum (x-\overline{X})^2}{n-1}}$

• Substitute the value of $s^2=443.33$

• $s=\sqrt{443.33}$
• $=21.05$

Therefore standard deviation s=21.05