Question

The median and modal profits for the following data
(
X): below 5 below 10 below 15 below 20 below 25 below 30

(f): 10 25 45 55 62 65

are

(a) 11.60 and 11.50
(b) ` 11556 and ` 11267

(c) ` 11875 and ` 11667 ✔️
(d) 11.50 and 11.67.

Please give full explanation (along with how to convert above improper Class Interval into a proper Class Interval)

​

Answer 1

Given : X): below 5 below 10 below 15 below 20 below 25 below 30

(f): 10 25 45 55 62 65  

To find :  Median & Mode

Solution:

                 cf                  f

0 - 5           10                10

5 - 10          25               15

10-15          45                20

15-20          55                10

20-25         62                7

25-30         65                 3

Median 65/2  lies in     10 - 15

Median =  10   + 5 *  ( 65/2 - 25) / (20)

= 10 + 1.875

= 11.875

Mode   ( max f = 20 ) lies in 10 - 15

Mode  = 10  + 5 *  ( 20 - 15)/ (20 - 15 + 20 - 10)

= 10 + 5 * 5 / 15

= 10 + 1.667

= 11.667

Median =   11.875

Mode = 11.667

option c is correct

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