Question

The median of the following data is 52.5 .Find the value of f1 and f2 if the total frequency is 100 .
Class interval frequency
0 - 10. 3
10 - 20. 5
20-30. F1
30-40. 12
40-50. 17
50-60. 20
60-70. F2
70-80. 9
80-90. 7
90-100. 4

Answer 1

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Answer 2

Answer:

$f_1=8\:\:and\:\:f_2=15$

Step-by-step explanation:

Given: Continuous frequency distribution table

           Median = 52.5   &  Total Frequency = 100

To find : $f_1\:\:and\:\:f_2$

Table with cf is attached.

from table,

$77+f_1+f_2=100$ .............................. (1)

Now we use median formula,

$Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

Median Class = 50 - 60

⇒ l = 50 , N = 100 , cf = $37+f_1$ , f = 20 , h = 10

$52.5=50+\frac{50-(37+f_1)}{20}\times10$

$52.5-50=\frac{50-37-f_1}{2}$

$2.5\times2=13-f_1$

$f_1=13-5$

$f_1=8$

Now putting this value in (1) we get,

$77+8+f_2=100$

$f_2=100-85$

$f_2=15$

Therefore, $f_1=8\:\:and\:\:f_2=15$