Question

The number of filler units sold in 5 consecutive days are 5, 8, 10, 12, 15. Find the standard deviation using Assumed mean method.

• A. 4.42
• B. 5.23
• C. 6.59
• D. 8.25

Answer 1

The correct option is A 4.42

Mean
$=\frac{5+8+10+12+15}{5}=\frac{50}{5}=10$

Hence, use take the Assumed Mean, A = 10, n = 5.

$\begin{array}{ccc}xi& di=xi-A& d{i}^2\\ & =xi-10& \\ 5& -5& 25\\ 8& -2& 4\\ 10& 0& 0\\ 12& 2& 4\\ 15& 5& 25\\ & \sum di=0& \sum d{i}^2=98\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum d{i}^2}{n}-(\frac{\sum di}{n}{)}^2}$

$=\sqrt{\frac{98}{5}-\frac{0}{5}}=\sqrt{19.6}\simeq 4.42$