Question

Obtain an inclusive continuous frequency distribution from the following data.
Lower boundary point or 44.5 49.5 54.5 59.5 64.5 69.5
74.5
79.5
more than that
Cumulative frequency
500
470
390
290
240
90
10
0
Obtain an exclusive continuous frequency distribution from the following data​

Answer 1

Explanation:

Here, the frequency table is given in inclusive form. So we first transform it into exclusive form by subtracting and adding h/2 to the lower and upper limits respectively of each class, whereh denotes the difference of lower and upper limit of a class and the upper limit of the previous class.

Transforming the above table into exclusive form and preparing the cumulative frequency table, we get

Weekly wages (in Rs.) No. of workers Cumulative frequency

59.5- 69.5 5 5

69.5- 79.5 15 20

79.5- 89.5 20 40

89.5- 99.5 30 70

99.5- 109.5 20 90

109.5- 119.5 8 98

N=∑fi=98

We have,

N=98.∴N/2=49

The cumulative frequency just greater than N/2 is 70 and corrssponding class is 89.5−99.5,So,89.5−99.5 is the median class.

∴l=89.5,h=10,f=30,andF=40

Now, Median =l+f2N−f×h

⇒Median=89.5+3049−40×10=92.5