Question

The mean height of 50 student of a college is 68 inches. The height of 30 students is given below. Find the mean height of the remaining 20 students.

Height (in inches)	64	66	68	70	72
Frequency	4	12	4	8	2

Answer 1

Height (X)	Frequency (f)	fX
64 66 68 70 72	4 12 4 8 2	256 792 272 560 144
	$\mathit{\Sigma }\mathit{f}$=30	$\mathit{\Sigma }\mathit{f}{\mathit{X}}_{\mathbf{30}}$=2024

Given:
Σf = 50

${\overline{X}}_{50}=68$

$\Sigma f{X}_{50}={\overline{X}}_{50}\times \Sigma f=68\times 50=3400$
ΣfX of remaining 20 students

$\Sigma f{X}_{20}$= $\Sigma f{X}_{50}-\Sigma f{X}_{30}$=3400 − 2024 = 1376

$\overline{\mathrm{X}}\mathrm{of}20\mathrm{students}=\frac{\Sigma f{X}_{20}}{\Sigma f}=\frac{1376}{20}=68.8\mathrm{inches}$
Hence, mean height of 20 students is 68.8 inches