Question

Calculate the median for the following data:
Class interval:-5-10,10-15,15-20,20-25,25-30,30-35,35-40
Frequency:-2,12,2,4,3,4,3
Cumulative Frequency:2,14,16,20,23,27,30​

Answer 1

Answer:

(Class interval) (f) (cf)

(5-10) (2) (2)

(10-15) (12) (14)

(15-20) (2) (16)

(20-25) (4) (20)

(25-30) (3) (23)

(30-35) (4) (27)

(35-40) (3) (30)

N = 30

Now N = 30 = Ef(sigmaf)

N/2 = 30/2 = 15

The cumulative frequency just greater than 15 is 16 and the corresponding class is 15-20.

Thus, the median class is 15-20.

So, l = 15, h = 5, f = 2, cf = 14, N/2 = 15

Now,

Median = M =

$= l + (h \times ((n \div 2) - cf) \div f)$

$= 15 + (5 \times (15 - 14) \div 2) \\ = 15 + (5 \times 1 \div 2) \\ = 15 + (5 \times 0.5) \\ = 15 + 2.5 \\ = 17.5$