Question

Calculate Median for the following data.
Class Interval
5-15
15-25
25-35
35-45
45-55
55-65
Frequency
6
11
21
23
14
5​

Answer 1

Given Data:•

$\boxed{\begin{array}{c|c} \bf{Class\:Interval} & \bf{Frequency} \\ \cline{1-2} \:\:\sf{5-15} & \sf{6} \\ \sf{15-25} & \sf{11} \\ \sf{25-35} & \sf{21} \\ \sf{35-45} & \sf{23} \\ \sf{45-55} & \sf{14} \\ \sf{55-65} & \sf{5} \end{array}}$

To Find:-

• Median of the data.

Solution:-

Firstly let us find the Cumulative Frequency of the given data:-

$\boxed{\begin{array}{c|c|c} \bf{Class\:Interval} & \bf{Frequency} & \bf{Cumulative\:Frequency} \\ \cline{1-3}\:\: \sf{5 - 15} & \sf{6} & \sf{6} \\ \sf{15-25} & \sf{11} & \sf{17} \\ \sf{25-35} & \sf{21} & \sf{38} \\ \sf{35-45} & \sf{23} & \sf{61} \\ \sf{45-55} & \sf{14} & \sf{75} \\ \sf{55-65} & \sf{5} & \sf{80}\end{array}}$

From the given data we can clearly see that the class 35 - 45 has the greatest frequency of 23.

∴ The median class is 35 - 45.

We already know:-

• $\dag{\boxed{\bf{\pink{Median = l + \bigg(\dfrac{\dfrac{n}{2} - cf}{f}\bigg) \times h}}}}$

Where:-

• l = Lower limit of the median class
• n = number of observations
• cf = cumulative frequency of class preceding the median class
• f = frequency of the median class
• h = size of class.

Now,

We have:-

• l = 35
• n = 80
• cf = 38
• f = 23
• h = 45 - 35 = 10

Putting all the values in the formula:-

$\sf{Median = 35 + \bigg(\dfrac{\dfrac{80}{2} - 38}{23}\bigg) \times 10}$

$= \sf{Median = 35 + \dfrac{40 - 38}{23} \times 10}$

$= \sf{Median = 35 + \dfrac{2\times 10}{23}}$

$= \sf{Median = 35 + \dfrac{20}{23}}$

$= \sf{Median = 35 + 0.87}$

$= \sf{Median = 35.87}$

∴ Median of the given data is 35.87

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