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Obtain an exclusive continuous frequency distribution from the following data. Less than weight (kg.) 30 35 40 45 50 55 60 65 70 Cumulative frequency 0 17 25 40 48 54 57 59 60

Vidyadip · Accepted Answer

Given data is ‘less than’ type cumulative frequency distribution.
Class length = Difference between two adjoining upper boundary points $= 35 – 30 = 5$
Now, lower boundary point of a class = upper boundary point – class length
∴ for initial class, lower boundary point $= 30 – 5 = 25$ and we get initial class $25 – 30.$
In this manner we will obtain class for each upper boundary point.
We find the frequency of a class as follows :
Frequency of a class = (‘less than ‘ cumulative frequency of a class) – (‘less than’ cumulative frequency of preceeding class)
Class frequency for upper boundary point $35 = 17 – 0 = 17$
In this manner, we will obtain the class frequency for each upper boundary point.
For the given data exclusive continuous frequency distribution is obtained as follows:

'Weight ‘less than’ in kg	‘Less than’ cumulative frequency cf	Weight(in kg)	Frequency f
$30$	$0$	$25-30$	$= 0$
$35$	$17$	$30-35$	$17- 0 = 17$
$40$	$25$	$35-40$	$25 – 17 = 8$
$45$	$40$	$40-45$	$40 – 25 = 15$
$50$	$48$	$45-50$	$48 – 40 = 8$
$55$	$54$	$50-55$	$54 – 48 = 6$
$60$	$57$	$55-60$	$57 – 54 = 3$
$65$	$59$	$60-65$	$59 – 57 = 2$
$70$	$60$	$65-70$	$60 – 59 = 1$
$–$	$–$	Total	$n = 60$

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Less than weight (kg.)	$30$	$35$	$40$	$45$	$50$	$55$	$60$	$65$	$70$
Cumulative frequency	$0$	$17$	$25$	$40$	$48$	$54$	$57$	$59$	$60$

Presentation of data — Statistics STD 11 Commerce — Question

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