Question

Calculate the median for following frequency distribution class interval = 1-4,5-8,9-12,13-16,17-20,21-24,25-28,29-32,33-36,37-40 frequency = 2,5,8,9,12,14,14,15,11,13

Answer 1

Answer:

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Answer 2

Median of the data is 24.9286

Step-by-step explanation:

Calculate Median for the given grouped data :

Class Interval          Frequency         cf

1-4                                  2                    2

5-8                                 5                    7

9-12                                8                  15

13-16                               9                  24

17-20                            12                  36

21-24                             14                 50

25-28                            14                 64

29-32                            15                 79

33-36                             11                 90

37-40                             13               103

                              n = 103

= Value of $(\frac{n}{2})th$ observation

= Value of $(\frac{103}{2})th$ observation

= Value of 51th observation

From the column of cumulative frequency cf, we find that the 51st observation lies in the class 25-28.

∴ The median class is 24.5-28.5.

Now,

L = lower boundary point of median class  = 24.5

n = Total frequency = 103

cf = Cumulative frequency of the class preceding the median class = 50

f = Frequency of the median class = 14

c = class length of median class  = 4

Median  $M=L+\frac{\frac{n}{2}-cf}{f}\times c$

$=24.5+\frac{51.5-50}{14}\times 4$

$=24.5+\frac{1.5}{14}\times 4$

= 24.5 + 0.4286

= 24.9286

Median of the data is 24.9286

Learn more about median of grouped data : https://brainly.in/question/15572413