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If the Median of the Following Frequency Distribution is 32.5. Find the Values of F 1 and F 2. - Mathematics

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Sum

If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Total
Frequency f1 5 9 12 f2 3 2 40
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Solution

Given: Median = 32.5
We prepare the cumulative frequency table, as given below.

Class interval: Frequency: (fi) Cumulative frequency (c.f.)
0-10 f1 f1
10-20 5 5 + f1
20-30 9 14 + f1
30-40 12 26 +f1
40-50 f2 26 +f1 + f2
50-60 3 29 + f1 + f2
60-70 2 31 + f1 + f2
  N = 40 = 31 + f1 +f2  

Now, we have
N = 40
31 + f1 + f2 = 40
f2 = 9 - f   ........(1)

Also, `("N")/(2) = 20`

Since median = 32.5 so the median class is 30 - 40.
Here, l = 30, f = 12 , F = 14 + f1 and h = 10

We know that

Median = `"l" + {{("N")/(2) -"F")/("f")} xx "h"`

`32.5 = 30 + {(20-(14+"f"_1))/(12)} xx 10`

`2.5 = ((6 - "f"_1) xx 10)/(12)`

2.5 x 12 = 60 - 10`"f"_1`

`"f"_1 = (30)/(10)`

= 3

Putting the value of `f_1` in (1), we get

`"f"_2` = 9 - 3

= 6
Hence, the missing frequencies are 3 and 6.

Concept: Graphical Representation of Cumulative Frequency Distribution
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