Question

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is :

• A. 16
• B. 22
• C. 20
• D. 18

Hint:

Find \(\sum x^2\) from the old variance and mean, add the new student, and recompute mean and variance.

Answer 1

The Correct Option is C

For 5 students: \(\frac{\sum x^2}{5} - 150^2 = 18 \Rightarrow \sum x^2 = 5(22500 + 18) = 112590\). Also \(\sum x = 750\).
Adding 156: \(\sum x = 906\), \(\sum x^2 = 112590 + 156^2 = 112590 + 24336 = 136926\).
New mean \(= \frac{906}{6} = 151\).
New variance \(= \frac{136926}{6} - 151^2 = 22821 - 22801 = 20\).
Answer: (3) 20