Q.Find the Variance and Standard Deviation of the data: 3, 6, 9, 12, 15.

Standard Deviation is the square root of the mean of the squared deviations of every value from the arithmetic mean. …

Step 1 — Compute the mean.

Step 2 — Compute $(x-\overline{x})^2$ for each value.

$\sum(x-\overline{x})^2 = 36+9+0+9+36 = 90$ …

Step-deviation method (verification): taking assumed mean $A=9$ and width $h=3$ (the values are evenly spaced 3 apart), $d=\frac{x-9}{3}$ gives $d$-values $-2,-1,0,1,2$, so $\sum d=0$ and $\sum d^2=4+1+0+1+4=10$. Then $$\sigma = h\sqrt{\dfrac{\sum d^2}{n}-\left(\dfrac{\sum d}{n …

Dividing by $n$ before taking the square root in the wrong place (confusing $\sqrt{\sum(x-\overline{x})^2}/n$ with the correct $\sqrt{\sum(x-\overline{x})^2/n}$); in the s …