Question

Sometimes I buy M&M’s instead of peanuts (like I did in the example yesterday). Find the

SAMPLE standard deviation of the number of chocolates in these six bags. You are more than welcome to create a chart below the data to help you find the solution.

21, 30, 25, 19, 24, 28

Answer 1

Here the given data is as follows $21,30,25,19,24,28$

Number of observation $N=6$

Mean of the above data $\mu =\frac{\Sigma X_i}{N}=\frac{(21+30+25+19+24+28)}{6}=24.5$

Standard deviation of data $\sigma =\sqrt{\frac{\Sigma (X_i-\mu)^2}{N}}$

For this we draw a table below

Therefore Standard Deviation($\sigma$ ) $=\sqrt {\frac {(12.25+30.25+0.25+30.25+0.25+12.25)}{6}}$

$=\sqrt{\frac{85.5}{6}}=\sqrt{14.25}$ $\approx 3.77$ (correct upto two decimal places)

Hence required Standard Deviation ($\sigma$) $=3.77$ (approximately).