Find the mode of the following data 0 20
Asked by admin @ in Math viewed by 369 People
Find the mean, median and mode of the following data:
Class
0 – 20
20 – 40
40 – 60
60 – 80
80 – 100
100 – 120
120 – 140
Frequency
6
8
10
12
6
5
3
Answered by admin @
SOLUTION :
FREQUENCY DISTRIBUTION TABLE is in the attachment
For MODE :
Here the maximum frequency is 12, and the class corresponding to this frequency is 60 – 80. So the modal class is 60 - 80.
Therefore, l = 60, h = 20, f1= 12, f0= 10 , f2 = 6
Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h
= 60 + [(12 - 10)/(2 × 12 - 10 – 6) ] ×20
= 60 + [2 × 20)/(24 - 16)]
= 60 + [40/ 8]
= 60 + 5
= 65
MODE = 65
Hence, the mode of the data is 65 .
MEAN :
From the table : Σfi = 50 , Σfixi = 3120
Mean = Σfixi /Σfi
Mean = 3120/50 = 312/5 = 62.4
Hence, the Mean of the data is 62.4 .
For MEDIAN :
Here, n = 50
n/2 = 25
Since, the Cumulative frequency just greater than 25 is 36 and the corresponding class is 60 - 80 . Therefore 60 - 80 is the median class.
Here, l = 60 , f = 12 , c.f = 24, h = 20
MEDIAN = l + [(n/2 - cf )/f ] ×h
= 60 + [(25 - 24)/12] × 20
= 60 + [(1 × 20)/12]
= 60 + 20/12
= 60 + 5/3
= 60 + 1.66
= 61.66
Hence, the Median of the data is 61.66 .
★★ Mode = l + (f1-f0/2f1-f0-f2) ×h
l = lower limit of the modal class
h = size of the class intervals
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeed in the modal class.
★★ MEDIAN = l + [(n/2 - cf )/f ] ×h
Where,
l = lower limit of the median class
n = number of observations
cf = cumulative frequency of class interval preceding the median class
f = frequency of median class
h = class size
HOPE THIS ANSWER WILL HELP YOU…
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