Question

Compute mean from the following data:

Marks	0 – 7	7 – 14	14 – 21	21 – 28	28 – 35	35 – 42	42 – 49
Number of Students	3	4	7	11	0	16	9

Answer 1

Class	Frequency (f)	Cumulative Frequency (cf)
0 – 7	3	3
7 – 14	4	7
14 – 21	7	14
21 - 28	11	25
28 – 35	0	25
35 – 42	16	41
42 – 49	9	50
	N = Σ𝑓 = 50

Now, N = 50 ⇒ `N/2` = 25.
The cumulative frequency just greater than 25 is 41 and the corresponding class is 35 – 42.
Thus, the median class is 35 – 42.
∴ l = 35, h = 7, f = 16, cf = c.f. of preceding class = 25 and `N/2` = 25.
Now,
Median =` l +((N/2−c_f)/f) × h`
Median `= 35 +  ((25 − 25)/16) xx 7`
= 35 + 0
= 35
Hence, the median age is 35 years.