Question

the following table gives the weekly expenditure of 200 families .Find the median of weekly expenditure.
weekly e2 0-1000.1 000-2000.
2000-3000.3000-4000.4000-5000
number of families 28. 46. 54.42.30​

Answer 1

The weekly median expenditure of families is 2481.48 Rs.

Given:

Weekly expend.__ number of families

0-1000________28

1000-2000_____46

2000-3000_____54

3000-4000_____42

4000-5000_____30

To find:

• Find the median of weekly expenditure.

Solution:

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

here,

l: lower limit of median class.

n/2= Half of total frequencies

cf: Cumulative frequency of previous to median class.

f: Frequency of median class.

h: height of class.

Step 1:

Make Cumulative frequency distribution table to find Median class.

$\begin{tabular}{|c|c|c|}\cline{1-3}Weekly\:Ex&Number\:of\:family&CF\\\cline{1-3}0-1000&28&28\\\cline{1-3}1000-2000&46&74\\\cline{1-3}2000-3000&54&128\\\cline{1-3}3000-4000&42&170\\\cline{1-3}4000-5000&30&200\\\cline{1-3}Total&200&\\\cline{1-3}\end{tabular}$

The class having CF 128 will be the median class.

as 128 is nearby greater to 100(i.e. n/2)

Step 2:

Write the values used in formula:

Median class : 2000-3000

l= 2000

cf:74

f:54

h=1000

n/2=100

Median$= 2000+ \left(\frac{ 100 - 74 }{54} \right) \times 1000$

or

$= 2000+ \left(\frac{ 26 }{54} \right) \times 1000$

or

$= 2000 + \frac{13000}{27}$

or

$= 2000 + 481.48$

or

$\bf Median= 2481.48$

Thus,

Weekly median expenditure is Rs 2481.48

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