Question

find the median for the following distribution Mark's classes 0to 10 10to 20 20to 30 30to 40 40to 50 no of students 2, 12 ,22 ,8 ,6​

Answer 1

Given Data:•

$\boxed{\begin{array}{c|c}\bf{Class\:Interval} & \bf{Frequency} \\ \sf{0-10} & \sf{2} \\ \sf{10-20} & \sf{12} \\ \sf{20-30} & \sf{22} \\ \sf{30-40} & \sf{8} \\ \sf{40-50} & \sf{6}\end{array}}$

To Find:-

• Median of the data

Solution:-

Firstly let us find the Cumulative

Frequency of the given data:-

$\boxed{\begin{array}{c|c|c} \bf{Class\:Interval} & \bf{Frequency} &\bf{Cumulative\:Frequency} \\ \dfrac{\qquad\qquad}{} & \dfrac{\qquad\qquad}{} & \dfrac{\qquad\qquad}{} \\ \sf{0 - 10} & \sf{2} &\sf{2} \\ \sf{10 - 20} & \sf{12} & \sf{14} \\ \sf{20-30} & \sf{22} & \sf{36} \\ \sf{30-40} & \sf{8} & \sf{44} \\ \sf{40-50} & \sf{6} & \sf \: 50\end{array}}$

From the given data we can clearly see that the class 20 - 30 has the greatest frequency of 22.

∴ The median class is 20 - 30.

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 = 20
• n = 50
• cf = 14
• f = 22
• h = 30 - 20 = 10

Putting all the values in the formula:-

$\sf{Median = 20 + \bigg(\dfrac{\dfrac{50}{2} - 14}{22}\bigg) \times 10}$

$= \sf{Median = 20+ \dfrac{25- 14}{22} \times 10}$

$= \sf{Median = 20+ \dfrac{11\times 10}{22}}$

$= \sf{Median = 20 + \dfrac{110}{22}}$

$= \sf{Median = 20 + 5}$

$= \sf{Median = 25}$

∴ Median of the given data is 25.

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Answer 2

Answer:

poop is good I think lol