convert the following frequency table into less than type cumulative frequency table and find the median also. Class 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70. frequency 5,15,20,23,17,11,9
Answers
Answer:
Median = 34.35
Step-by-step explanation:
Given :-
Class = 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70.
frequency = 5,15,20,23,17,11,9
To find :-
Convert the following frequency table into less than type cumulative frequency table ? find the median also.?
Solution :-
See the above attachment
From the table we have,
Less than cumulative frequencies are
5 ,20, 40 ,63 , 80 , 91 , 100
Sum of all frequencies = N = 100
=N/2 = 100/2 = 50
lower boundary of the median class = l = 30
frequency of the median class =f = 23
cumulative frequency of the class preceding the median class = cf = 40
Size of the class = 10
We know that
Median of the grouped data
M = l + [{(N/2) - cf}/f] × h
On Substituting these values in the above formula
=> M = 30 + [(50-40)/23]×10
=> M = 30 + (10/23)×10
=> M = 30+ (10×10)/23
=> M = 30+(100/23)
=> M = 30+4.347...
=> M = 30+4.35
=>M = 34.35
Therefore, M = 34.35
Answer :-
Less tha cumulative frequencies = 5 ,20, 40 ,63 , 80 , 91 , 100
Median for the given data = 34.35
Used formulae :-
Less than Cumulative Frequency:-
- The frequency obtained by adding successively the frequencies of all the previous classes including the class against which it is written is called less than cumulative frequency.
- The cumulate is started from the lowest to the highest size.
Median :-
- Median is the middle term of the given dats when it is arranged either ascending order or descending order.
- M = l+[{(N/2)-cf}/f] × h
Where,
- M = Median
- l = Lower boundary of the median class
- N = Total Frequencies
- cf = Cumulative frequency of the class preceding the median class.
- f = frequency of the median class
- h = class size.