Question

calculate the median of following
class frequency
20-30. 6
30-40. 10
40-50. 16
50-60. 18
60-70. 12
70-80. 10
80-90. 8​

Answer 1

Answer:

18 is the answer of the question

Answer 2

Answer:

Median = 50

Step-by-step explanation:

We are given the following frequency distribution below;

    Classes               Frequency (f)                 Cumulative frequency (cf)

     20 - 30                        5                                              5

    30 - 40                         15                                            20

   40 - 50                       25                                            45

     50 - 60                       20                                            65

     60 - 70                        7                                              72

     70 - 80                        8                                              80

     80 - 90                       10                                            90

                                   ∑f = 90  

Firstly, we will calculate \frac{N}{2}2N , (where N = ∑f), \frac{N}{2}2N = \frac{90}{2}290 = 45.

So, the value of cumulative frequency just greater than or equal to 45 is 45.

Therefore, median class is 40 - 50 .

Now, Median formula =  x_L + \frac{\frac{N}{2} -cf}{f_m}*cxL+fm2N−cf∗c  

where, x_LxL = lower limit of median class = 40

            N =  ∑f = 90   

           f_mfm = frequency of median class = 25

            cf = cumulative frequency just above the median class = 20

             c = width of class interval = 10

So, Median = 40 + \frac{\frac{90}{2} -20}{25}*1040+25290−20∗10

                   = 40 + 10 = 50 .

Therefore, Median of given distribution is 50

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