Question

Ci = 10-20 , 20-30 , 30-40 , 40-50,50-60
F = 15 , 30 , 45 , 12 , 18.
find mode of the following data.

Answer 1

If the median of the distribution given below is 28.5, find the values of x and y.

Class interval
Frequency
0-10
5
10-20
x
20-30
20
30-40
15
40-50
y
50-60
5
Total
x = 60

Forming the cumulative frequency table, we have

Class Interval (C.I.)
Frequency
c.f.
0-10
5
5
10-20
x
5 + x
20-30
20
25+ x
30-40
15
40 + x
40-50
y
40 + x + y
50-60
5
45 + x + y
Total
60


It is given that n = 60
45 + x + y = 60
x + y = 15
It is given that median is 28.5
So, the median lies in the group of 30-40
i.w. median class = 20 - 30
Thus, we have Median Class = 20 - 30

Now, substituting these values in the formula of Median, we get

Answer 2

Hiii friend,


CI = [ 10-20] [ 20-30] [30-40] [ 40-50] [50-60]

F = [ 15 ] [ 30 ] [ 45 ] [ 12 ] [ 18 ]

Now,


Maximum class frequency is 45

Modal class = 30-40

Lower limit of madal class (Xk) = 30

Frequency of the modal class (Fk) = 45

Frequency of the class preceding the modal class (Fk-1) =30

Frequency of the class succeeding the modal class ( Fk+1) = 12

Class size (H) = 10.

Therefore,

Mode = Xk+(Fk-Fk-1)
********* ______ × H
***********2Fk - Fk-1 - Fk+1


=>. 30 + (45-30/90-30-12) × 10

=> 30 + 150/48


=> 30 + 75/24

=> 30 + 3.12


=> 33.12

HENCE,


MODE = 33.12



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