Question

Compute median of the following data:

Mid-value:	115	125	135	145	155	165	175
Frequency:	12	15	20	16	10	16	11

Answer 1

Difference between mid-values = 125 – 115 = 10. So h = 10.

Class boundaries for 115: `115 ± 10/2` ⇒ 110 – 120.

Class Interval	Mid-value	Frequency (f)	Cumulative Frequency (cf)
110 – 120	115	12	12
120 – 130	125	15	27
130 – 140	135	20	47
140 – 150	145	16	63
150 – 160	155	10	73
160 – 170	165	16	89
170 – 180	175	11	100
Total (N)		100

N = 100, `N/2 = 50`.

The cumulative frequency just greater than 50 is 63, so the Median Class is 140 – 150.

l = 140, f = 16, cf = 47, h = 10.

Median = `l + ((N/2 - cf)/f) xx h`

= `140 + ((50 - 47)/16) xx 10`

= `140 + (3 xx 10)/16`

= `140 + 30/16`

= 140 + 1.875

= 141.875