The heights of six students in a class are 169 cm, 172 cm, 178 cm, 170 cm, 166

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.

Options:

A . 2.85

B . 3.46

C . 3.82

D . 4.15

Answer: Option C
:
C
Let 170 be the assumed mean (A).

\begin{matrix} 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{matrix}

σ = \sqrt{\frac{\sum D^{2}}{N} - {(\frac{\sum D}{N})}^{2}} = \sqrt{\frac{101}{6} - {(\frac{9}{6})}^{2}} = \sqrt{14.58} = 3.82

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