Question

6. Find out median from the following table:
Monthly Wages
80-100 100-110 110-120 120-130 130-150 150-180 180-200
(in Rs.):
50-80
No. of workers:
30
127
140
240
176
135
20
3
A fund is to be raised and it is decided that workers getting less than Rs. 120 should
contribute 5% of their wages and those getting more than Rs. 120 should contribute 10% of
their wages. What sum will be collected?
[Ans. M=115.77, Total Fund - 7261)
into​

Answer 1

Answer:

median =166 approximately

Answer 2

Correct Question

Find out the median from the following table:

$\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 50-80 \\ 80-100 \\100-110 \\110-120 \\ 120-130 \\ 130-150 \\ 150-180 \\ 180-200\end{tabular}$     $\begin{tabular}{c}\\ \underline{No. of Workers} \\ 30\\127\\140\\240\\176\\135\\20\\3\end{tabular}$

A fund is to be raised and it is decided that workers getting less than Rs. 120 should contribute 5% of their wages and those getting more than Rs. 120 should contribute 10% of their wages. What sum will be collected?

Answers

The median is Rs. 115.79 and the total funds collected is Rs. 7261.

Given

• Frequency Table
• workers getting less than Rs. 120 should contribute 5% of their wages to the fund.
• workers getting more than Rs. 120 should contribute 10% of their wages to the fund.

To Find

• Median
• Amount of funds collected

Solution

First, we need to make a cumulative frequency table

$\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 50-80 \\ 80-100 \\100-110 \\110-120 \\ 120-130 \\ 130-150 \\ 150-180 \\ 180-200\end{tabular}$  $\begin{tabular}{c}\\ \underline{No. of Workers} \\ 30\\127\\140\\240\\176\\135\\20\\3\end{tabular}$  $\begin{tabular}{c}\\ \underline{c.f} \\ 30\\157\\297\\537\\713\\848\\868\\871\end{tabular}$

Median

= l + (N/2 - c.f )/f X h

where,

l = lower limit of the median class

N = total frequency,

c.f = cumulative frequency of the class just before the median class

f = frequency of the median class

h = class size

A median class is that class whose cumulative frequency is just more than the value of N/2

Here,

N = 871

Hence N/2 = 435.5 = 436 (since humans cannot be in decimal)

Therefore,

median class = 110-120

Therefore,

l = 110

c.f = 297

f = 240

h = 10

Hence, median

= 110 + (436 - 297)/240 X 10

= 110 + 139/240 X 10

= 110 + 0.579 X 10

= 110 + 5.79

= Rs. 115.79

A cumulative frequency table is the less-than-frequency table of that data.

Here we see that

4 classes show wage data of wages less than Rs. 120

and,

4 classes show wage data of wages more than Rs. 120

Dividing them according to the criteria we get

Table 1-

 $\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 50-80 \\ 80-100 \\100-110 \\110-120\end{tabular}$  $\begin{tabular}{c}\\ \underline{No. of Workers} \\ 30\\127\\140\\240\\\end{tabular}$

and

Table 2-

 $\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 120-130 \\ 130-150 \\ 150-180 \\ 180-200\end{tabular}$  $\begin{tabular}{c}\\ \underline{No. of Workers} \\176\\135\\20\\3\end{tabular}$

Now we will take the class mark and multiply it with the frequencies of both tables. Thus we will get

Table 1-

  $\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 50-80 \\ 80-100 \\100-110 \\110-120\end{tabular}$     $\begin{tabular}{c}\\ \underline{X_1} \\ 65 \\ 90 \\105 \\115\end{tabular}$    $\begin{tabular}{c}\\ \underline{No. of Workers} \\ 30\\127\\140\\240\\\end{tabular}$     $\begin{tabular}{c}\\ \underline{X_1f_1} \\ 1950 \\ 11430 \\ 14700 \\27600 \\\end{tabular}$        

∑X₁f₁ = 55680

5% of ∑X₁f₁

= Rs. 2784

Table 2

   $\begin{tabular}{c}\\ \underline{Monthly Wages(in Rs.)} \\ 120-130 \\ 130-150 \\ 150-180 \\ 180-200\end{tabular}$   $\begin{tabular}{c}\\ \underline{X_2} \\ 125 \\ 140 \\ 165 \\ 190\end{tabular}$  $\begin{tabular}{c}\\ \underline{No. of Workers} \\176\\135\\20\\3\end{tabular}$    $\begin{tabular}{c}\\ \underline{X_2} \\22000 \\ 18900 \\ 3300 \\ 570\end{tabular}$

∑X₂f₂ = Rs. 44770

Therefore,

10% of ∑X₂f₂

= 10% of Rs. 44770

= Rs. 4477

Hence total funds collected

= Rs. 2784 + Rs. 4477

= Rs. 7261

Therefore, the median is Rs. 115.79 and the total funds collected is Rs.7261.

#SPJ2