5 students of a class have an average height 150 cm and variance 18 cm^2.

Question

5 students of a class have an average height 150 cm and variance 18 cm\^2. A new student, whose height is 156 cm, joined them. The variance (in cm\^2) of the height of these six students is:

Accepted Answer

$\sum_{i=1}^5 x_i = 750$; $\dfrac{\sum x_i^2}{5}-150^2=18 \implies \sum x_i^2 = 112590$

New mean: $\bar x_{new} = \dfrac{750+156}{6}=151$

$$\sigma_{new}^2 = \frac{112590+156^2}{6}-151^2 = 22821-22801=20$$

Solutions · 1