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Candidate Salary (in thousand) 25-35 35-45 45-55 55-65 65-75 75-85
Number of Employees 40 15 8 18 12 7


The median of given data (up to 2 decimals places) is:  


1. 39.90
2. 47.14
3. 41.66
4. 43.25

1 Answer

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Best answer
Correct Answer - Option 3 : 41.66

Concept:

Median of a grouped data is given by:

\(Median = l + \frac{\frac{N}{2}-F}{f}\times h\)        ----(1)

Where,

  • l = lower limit of the median class
  • f = frequency of the median class
  • F = cumulative frequency of the class preceding the median class
  • N = total number of observations
  • h = width of the median class

The class whose cumulative frequency is just greater than the value N/2 is called the median class.

Calculation:

Candidate Salary (in thousand) Number of Employees Cumulative frequency
25-35 40 40
35-45 15 55
45-55 8 63
55-65 18 81
65-75 12 93
75-85 7 100

 

Here, N = 100

⇒ N/2 = 100/2 = 50

∴ The median class is 35-45

So, l = 35, f = 15, F = 40, N = 100, h = 10

\(⇒ Median = 35 + \frac{50-40}{15}\times 10\)      [using(1)]

\(⇒ Median = 35 + \frac{10}{15}\times 10\)

⇒ Median = 35 + 6.66 = 41.66

Hence, median = 41.66

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