Question

W
subquestions
The median of the following data is 49.2. Find the values off, and 11-01
20 - 3030 - 40 40-50 50-60 60-70 70-800-90
Frequency
15 25 1 20 1 8 10
Marks​

Answer 1

The values of missing frequencies are 7 and 5.

Step-by-step explanation:

Given :

Median = 49.2

Cumulative frequency $\sum f_{i}=90$    

∴ $f_{1}+15+25+20+f_{2}+8+10=90$

$f_{1}+f_{2}+78=90$

$f_{1}+f_{2}=90-78=12 .......................(1)$

$\text {Median}=l+\frac{h}{f}\left(\frac{N}{2}-c\right)$

Where, l = is lower class of the median = 40

           h = Size of the class interval = 10

            f = frequency corresponding to the median class = 25

           N = sum of the frequencies = 90

            c = cumulative frequency preceding the median class = 15 +

Hence,

$49.2 = 40 + \frac{10}{25}(\frac{90}{2} - 15 + f_1)$

$49.2 - 40 = 0.4(30+f_1)$

$\frac{9.2}{0.4} = 30 + f_1$

∴ $f_1$ = 7

$f_2$ = 12 - 7 = 5 (from equation 1)

The missing frequencies  7 and 5.

The image of the correct question is attached with the answer.

To Learn More....

1. The mean of the following frequency distribution is 50 find the missing frequencies f1 and f2

Class 0-20 0-40 40-60 60-80 80-100

total  17 f1 32 f2 19 120

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2. The median of the following data is 20.75. find the missing frequencies x and y,if the total frequency is 100.

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