Draw the two ogives for the following frequency distribution of the weekly wages of (less than and more than) number of workers.
Weekly wages Number of workers
0 – 20 41
20 – 40 51
40 – 60 64
60 – 80 38
80 – 100 7
Hence find the value of median.
Answers
Concept:
The Less than cumulative frequency distribution can be obtained by adding the successive frequencies with the previous classes along with the class against which it is written. In this, the cumulate begins from the lowest to the highest size. Similarly, the more than cumulative frequency distribution can be obtained by subtracting all the proceeding frequencies from the sum of all the frequencies.
Given:
The frequency distribution of the weekly wages and number of workers is attached below.
Find:
Ogives for the less than and more than frequency distribution and the value of the median.
Solution:
The less than frequency and more than frequency are tabulated in the tables.
The less than and more than ogive graphs have been plotted and attached.
Median of the grouped data:
Median = l + [ { (n/2) - cf }× h ] / f
Where l is the lower limit of the median class, n is the number of observations, f is the frequency of the median class, h is the class size, cf is the cumulative frequency of class which is preceding the median class.
Median = 40 + [ { (201/2) - 64 }× 10 ] / 92 = 43.97
Hence, the value of the median is 43.97.
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