Look at the frequency distribution table given below: Class interval 35-45 45-55 55-65 65-75 Frequency 8 12…

Look at the frequency distribution table given below:

Class interval
35-45
45-55
55-65
65-75
Frequency
8
12
20
10

The median of the above distribution is:

  1. 59

  2. 56.5

  3. 58.5

  4. 57.5

Solution

Solution:

Class intervalClass interval
FrequencyFrequency
Cumulative frequencyCumulative frequency
35-45 
8
8
45-55
12
20
55-65
20
40
65-75
10
50
Here, \(\text{N}=50\Rightarrow\frac{\text{N}}{2}=25\)

The cumulaove frequency just greater than 25 is 40.

Hence, median class is 55-65.

Now, median \(=\text{l}+\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}\)

\(=55+\Big\{10\times\frac{(25-20)}{20}\Big\}\)

\(=55+2.5\)

\(=57.5\)

Asked in: School

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