Math, asked by adityasaini9412, 2 months ago

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

Answered by tennetiraj86
1

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.
Attachments:
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