Question

Using step deviation method, find the median of the following data:

Class interval | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120

Frequency | 13 | 15 | 20 | 19 | 17 | 16
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Also, by using Empirical formula, find the mean if mode of the above data is 65​

Answer 1

Answer:

Step-by-step explanation:

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

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