Question

The frequency distribution table below shows the height of 50 students of grade 10. 

Heights (in cm)	138	139	140	141	142
Frequency	6	11	16	10	7

Find the median, the upper quartile and the lower quartile of the heights. 

Answer 1

Height (in cm)	Frequency (f)	Cumulative frequency
138	6	6
139	11	17
140	16	33
141	10	43
142	7	50

No. of terms = 50 

The mean of 25^th and 26^th term is the median 

25^th and 26^th  terms lay under 140 and 140 

median = `(140 + 140)/2 = 140`

Hence, Median = 140 

Upper Quartile (Q₃) = `(n xx 3)/4 = (50 xx 3)/4` = 37.5^th term = 141

Lower Quartile (Q₁) = `n/4 = 50/4` = 12.5^th term = 139

Upper Quartile = 141 and Lower Quartile = 139