Question

5. Find the standard deviation of the average temperatures recorded over a five-day period last winter with the sample data : 18, 22, 19, 25, 10​

Answer 1

Sum of all number

Numbers in sum

= 18 + 22 + 19 + 25 + 10 / 5

94 / 5 = 18.8

Answer 2

Given is data for average temperature for five days, Find their standard deviation.

Explanation:

• The standard deviation of data is the measure of dispersion/ spreading of the data value about its mean.  
• It can be mathematically defined as the square root of the variance of the data.
• Here we have, $X={18,\ 22,\ 19,\ 25,\ 10}, \ \ \ N=5$
• The variance of data can be expressed as the expectation of $X\ and\ X^2$ as, $\sigma^2=E(X^2)-(E(X))^2$
• Now we have, $E(X)=\frac{18+22+19+25+10}{5}=18.8\ \ \ \ \ \ \ ->(E(X))^2=353.44\\ E(X^2)=\frac{18^2+22^2+19^2+25^2+10^2}{5}=378.8$
• From the above values we get the variance, $\sigma^2=378.8-353.44\ \ \ \ \ \ ->\sigma^2=25.36$    
• Hence, the standard deviation of the given data is $\sigma=5.036$ (approx.)