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:

• A. 16
• B. 22
• C. 20
• D. 18

Answer 1

Answer: (C)

20

Answer 2

To solve this problem:

1. Calculate the sum of heights and the sum of squares of heights for the initial group of 5 students using the given average height and variance.
2. Incorporate the new student's height to find the new sum of heights and sum of squares of heights for all 6 students.
3. Calculate the new mean and variance.

• Sum of heights of initial 5 students = $5 \times 150 = 750$ cm
• Sum of squares of heights of initial 5 students = $5 \times (18 + 150^2) = 112590$
• New sum of heights = $750 + 156 = 906$ cm
• New sum of squares of heights = $112590 + 156^2 = 136926$
• New average height = $\frac{906}{6} = 151$ cm
• New variance = $\frac{136926}{6} - (151)^2 = 22821 - 22801 = 20$ cm$^2$

Therefore, the variance of the height of these six students is 20 cm$^2$.