Question

find the median wage of female workers engaged in housekeeping of a particular locality whose data is given below Wages no.of female workers 3500. 13 3800. 12 4100. 25 4500. 17 5500 12 6500. 15 7000. 6

Answer 1

Wages                 3500    3800  4100  4500  5500  6500  7000
No. Of workers       13        12      25     17      12       15      6
Cumulative freq.     13        25      50     67      79       94      100

The total no. of women workers = 100

the median is the average of the 50th and the 51st woman

From the cumulative frequency:
The 50th woman earns = 4100
The 51st woman earns = 4500

The median = (4100 + 4500)/2 = 4300

Answer 2

Answer:

The median wage of female workers engaged in housekeeping is Rs 4300.

Step-by-step explanation:

As per the data given in the question,

We have the following table,

Wages             No. of female workers      Cumulative frequency

3500                              13                                          13

3800                              12                                          25

4100                               25                                         50

4500                              17                                          67

5500                              12                                          79

6500                              15                                          94

7000                               6                                          100

Since total number of female workers is $n= 100$ which is even,

so, median will be average of $(n/2)th$ and $(n/2\:+1)th$ term.

$Median = [(n/2)th + (n/2\:+1)th] \div 2$

$Median = [50th\:term + 51th \:term]\div 2$

From the observation table,

50th term is 4100 and 51th term is 4500.

So, $median = (4100+4500)\div2$

$Median = Rs\: 4300$

∴The median wage of female workers engaged in housekeeping is Rs 4300.

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