Question

find the median and mode of this data.
class interval frequency
0-20 6
20-40 8
40-60 10
60-80 12
80-100 6
100-120 5
120-140 3

Answer 1

Answer:

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 .

Step-by-step explanation: