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Problem: mode {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} [ Calculator, Method and examples ]

Solution:
Your problem -> mode {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}}

 Class(1) Frequency (f)(2) Mid value (x)(3) f*x(4)=(2)xx(3) cf(6) 1 3 1 3 3 2 4 2 8 7 5 10 5 50 17 6 - 10 23 8 184 40 10 - 20 20 15 300 60 20 - 30 20 25 500 80 30 - 50 15 40 600 95 50 - 70 3 60 180 98 70 - 100 2 85 170 100 --- --- --- --- --- n = 100 ----- sum f*x=1995 -----

Mean bar x = (sum fx)/n

=1995/100

=19.95

To find Median Class
= value of (n/2)^(th) observation

= value of (100/2)^(th) observation

= value of 50^(th) observation

From the column of cumulative frequency cf, we find that the 50^(th) observation lies in the class 10 - 20.

:. The median class is 10 - 20.

Now,
:. L = lower boundary point of median class =10

:. n = Total frequency =100

:. cf = Cumulative frequency of the class preceding the median class =40

:. f = Frequency of the median class =20

:. c = class length of median class =10

Median M = L + (n/2 - cf)/f * c

=10 + (50 - 40)/20 * 10

=10 + (10)/20 * 10

=10 + 5

=15

Mode :
The given data is uni-model.
Hence, we find the mode with the help of the formula.
Z = 3M - 2 bar x

=3 * 15 - 2 * 19.95

=45 - 39.9

=5.1

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