Question

Find the variance and standard deviation for the following data: 2, 3, 6, 8, 10, 13, 16.


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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given: data: 2, 3, 6, 8, 10, 13, 16.

to find: Standard deviation and Variance.

Arranging the given number in ascending order:

• as the data is given in the right order we will retain the same.

$Mean(x) = \frac{2+3+6+8+10+13+16}{7}$

              =  $\frac{58}{7}$

              = $8.28$

hence, the mean of the given data is 8.28

we know that,

$variance$= $\sqrt \frac{{E (x_{1}-x_{2} } )^{2}}{n}$

$standard deviation=\frac{{E (x_{1}-x_{2} } )^{2}}{n}$

$variance= \frac{(2-8)^{2} +(3-8)^{2}+(6-8)^{2} +(8-8)^{2} + (10-8)^{2} +(13-8)^{2}+(16-8)^{2}}{7}$

              = $\frac{(-6)^{2} +(-5)^{2} +(-2)^{2} +(-0)^{2}(-6)^{2} +(5)^{2}+(8)^{2}}{7}$

             =  $\frac{36+25+4+0+36+25+64}{7}$

             = $\frac{190}{7}$

             = $27.0142$

variation = 27.0142

Standard deviation = $\sqrt{27.0142}$

                               = $5.197$

hence the standard deviation of the data is = 5.197

hence the variance of the given data is = 27.0142

and the standard deviation of the data is = 5.197