Question

The heights of six students in a class are 169 cm, 172 cm, 178 cm, 170 cm, 166 cm and 174 cm. Find the standard deviation of heights using the assumed mean method.

• A. 2.85
• B. 3.46
• C. 3.82
• D. 4.15

Answer 1

The correct option is C 3.82

Let 170 be the assumed mean (A).

$\begin{array}{ccc}X& D=X-A& D^2\\ 169& -1& 1\\ 172& 2& 4\\ 178& 8& 64\\ 170& 0& 0\\ 166& -4& 16\\ 174& 4& 16\\ & \sum D=9& \sum D^2=101\end{array}$

$\sigma =\sqrt{\frac{\sum D^2}{N}-{\left(\frac{\sum D}{N}\right)}^2}=\sqrt{\frac{101}{6}-{\left(\frac{9}{6}\right)}^2}=\sqrt{14.58}=3.82$