Question

Calculate the median for the following data:

Class	19 – 25	26 – 32	33 – 39	40 – 46	47 – 53	54 - 60
Frequency	35	96	68	102	35	4

Answer 1

First, we will convert the data into exclusive form.

Class	Frequency (f)	Cumulative Frequency (cf)
18.5 – 25.5	35	35
25.5 – 32.5	96	131
32.5 – 39.5	68	199
39.5 – 46.5	102	301
46.5 – 53.5	35	336
53.5 – 60.5	4	340
	N = Σ𝑓 = 340

Now, N = 340
`⇒ N/2 = 170`.
The cumulative frequency just greater than 170 is 199 and the corresponding class is 32.5 – 39.5.
Thus, the median class is 32.5 – 39.5.
∴ l = 32.5, h = 7, f = 68, cf = c.f. of preceding class = 131 and `N/2` = 170.
∴ Median, `M = l + {h×((N/2−cf)/f)}`
           `= 32.5 + {7 × ((170 − 131)/68)}`
           = 32.5 + 4.01
            = 36.51
Hence, the median = 36.51.