Question

Find the median for the following data :CI is 5-15,15-25,25-35,35-45,45-55,55-65 And its frequency is:
6,11,21,23,14,5

Answer 1

A+fd/f

Use this formula

Find .

Answer 2

Answer:

The median is 19.7

Step-by-step explanation:

Given data is:

Class interval       Frequency              Cumulative Frequency

   5 - 15                        6                                       6

  15 - 25                       11                                      17

  25 - 35                      21                                     38

  35 - 45                      23                                     61

  45 - 55                      14                                      75

  55 - 65                       5                                       80

We know that the median class is the class at middle frequency

=> 80/2 = 40

As 40 will lie in the interval 35 - 45, it is the median class.

We know that median = l + $(\frac{\frac{n}{2} -cf }{f} )$ * h

where

 l = lower limit of the median class

n = number of observations

cf = the cumulative frequency of class before the median class.

 f = frequency of the median class

h = size of the class interval

On substituting the values,

Median = 35 +  $(\frac{\frac{6}{2} - 38 }{23} )$ * 10

             = 35 +  $(\frac{3- 38 }{23} )$ * 10

             = 35 +  $(\frac{- 35 }{23} )$ * 10

             = 35 + (-15.217)

             = 19.783

Therefore, the median is 19.78