Question

find the variance and standard deviation of the highest temperatures recorded in eight specific states: 112, 100, 127, 120, 134, 118, 105, and 110.

Answer 1

The variance and standard deviation of the highest temperatures recorded in eight specific states are 108.89 and 10.435 respectively.

The given data is 112, 100, 127, 120, 134, 118, 105, and 110.

We need to find the variance and standard deviation of the highest temperatures recorded in eight specific states.

What are variance and standard deviation?

Variance and Standard Deviation are the two important measurements in statistics. Variance is a measure of how data points vary from the mean, whereas standard deviation is the measure of the distribution of statistical data.

We know that, variance $=\frac{(x_{i}-x )}{n}$ , Where x is mean and n is the number of observations.

Now, the average of given numbers $=\frac{112+100+127+120+134+118+105+110}{8} =115.75$

Variance$=\frac{(-3.75)^{2} +(-15.75)^{2}+(11.5)^{2}+(4.25)^{2}+(18.25)^{2}+(2.25)^{2}+(-10.75)^{2}+(2.25)^{2}}{8}$

$=\frac{14.0625+248.0625+132.25+18.0625+333.0625+5.0625+115.5625+5.0625}{8}= \frac{871.1875}{8}=108.89$

We know that, standard deviation $=\sqrt{Variance} =\sqrt{108.89} =10.435$.

Therefore, the variance and standard deviation of the highest temperatures recorded in eight specific states are 108.89 and 10.435 respectively.

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