Question

Find the median from the following data:

Class	1 – 5	6 – 10	11 – 15	16 – 20	21 – 25	26 – 30	31 – 35	35 – 40	40 – 45
Frequency	7	10	16	32	24	16	11	5	2

 

Answer 1

Converting into exclusive form, we get:

Class	Frequency (f)	Cumulative Frequency (cf)
0.5 – 5.5	7	7
5.5 – 10.5	10	17
10.5 – 15.5	16	33
15.5 – 20.5	32	65
20.5 – 25.5	24	89
25.5 – 30.5	16	105
30.5 – 35.5	11	116
35.5 – 40.5	5	121
40.5 – 45.5	2	123
	N = Σ𝑓 = 123

Now, N = 123
⇒` N/2` = 61.5.
The cumulative frequency just greater than 61.5 is 65 and the corresponding class is 15.5 – 20.5.
Thus, the median class is 15.5 – 20.5.
∴ l = 15.5, h = 5, f = 32, cf = c.f. of preceding class = 33 and `N/2` = 61.5.
∴ Median,` M = l + {h×((N/2−f)/f)}`
             `= 15.5 + {5 × ((61.5 − 33)/32)}`
              = 15.5 + 4.45
              = 19.95
 Hence, median = 19.95.