Question

find the median of the following data: marks obtained 0-10 10-20 20-30 30-40 40-50 50-60
frequency 8,10,12,22,30,18​

Answer 1

Step-by-step explanation:

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Answer 2

The median of the given data is 39.09

Given:

$\begin{tabular}{|c|c|c|}\cline{1-2}Marks\:obtained&freq\\\cline{1-2}0-10&8\\\cline{1-2}10-20&10\\\cline{1-2}20-30&12\\\cline{1-2}30-40&22\\\cline{1-2}40-50&30\\\cline{1-2}50-60&18\\\cline{1-2}\end{tabular}$

To find: Median of data.

Solution:

Formula of CF for grouped data:

$\bf Median = l + \left( \frac{ \frac{n}{2}-cf }{f} \right) h$

where

l= lower limit of median class

cf= cumulative frequency of succeeding of median class

n/2= half of total frequency

f=frequency of median class

h= height of classes

Step 1:

Construct table for CF.

$\begin{tabular}{|c|c|c|c|}\cline{1-3}Marks\:obtained&freq& CF\\\cline{1-3}0-10&8& 8\\\cline{1-3}10-20&10& 18\\\cline{1-3}20-30&12&30\\\cline{1-3}\bf 30-40&22& 52\\\cline{1-3}40-50&30&82\\\cline{1-3}50-60&18&100\\\cline{1-3}Total&100&\\\cline{1-3}\end{tabular}$

Step 2:

Write all values required for median calculation.

n/2= 50

Median class is 30-40

l= 30

cf=30

h=10

f=22

Step 3:

put the values in the formula.

$Median = 30+ \left( \frac{50-30 }{22} \right) 10$

or

$Median = 30+ \left( \frac{20 }{22} \right) 10$

or

$Median = 30+9.09$

or

$\bf Median = 39.09$

Thus,

Median of given data is 39.09.

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