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Maths-

General

Easy

Question

The median from the following data is

83.17
84.08
82.17
85.67

hint Hint:

We are given a table. We have to find the median of the data. Median is the middle number of the data.

The correct answer is: 84.08

We will use the formula of median to find the answer.
$M space equals space l space plus space fraction numerator begin display style N over 2 end style space minus space c. f over denominator f end fraction cross times space w$
From the data, we find the median class. It is range whose cumulative frequency is greater than the total cumulative frequency divided by 2 i.e N/2.
N is total cumulative frequency.
c.f is the cumulative frequency of a class previous to median class.
f is the frequency of the median class.
w is the width of the class.
l is the lower limit of the median class.
Before finding median we will find the cumulative frequency. The frequency of first term is added to the second, then that value is added to next frequency and so on.

Wages No of workers Cummulative
Frequency

50 - 59 15 15

60 - 69 40 40 + 15 = 55

70 - 79 50 55 + 50 = 105

80 - 89 60 105 + 60 = 165

90 - 99 45 165 + 45 = 210

100 - 109 40 210 + 40 = 250

110 - 119 15 250 + 15 = 265

So, the value of N here is 265
$N over 2 equals space 265 over 2 N over 2 equals space 132.5$
The frequency greater and closest to 132.5 is 165.
The median class is 80 - 89
l = 80
c.f = 105
f = 60
w = 10
Substituting all the values in the formula we get,
$M space equals space 80 space plus space fraction numerator 132.5 space minus space 105 over denominator 80 end fraction cross times space 10 space space space space equals space 80 space plus space fraction numerator 27.5 over denominator 80 end fraction cross times space 10 space space space space equals space 80 space plus space 3.43 space space space space equals 83.43 space space space space space$
The value is closest to 84.08
So, the right option is 84.08

For such questions, we should know the formula to find a median

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