find the median of following data :
class interval :- 0-20 ,20-40,40-60,60-80,80-100,100-120,120-140
frequency:- 6,8,10,12,6,5,3
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- Median of given data
As we know that
→ Median = l + {h × (N/2 - cf/f)}
Where
- l = lower limit
- h = width of median class
- cf = cumulative frequency
- N = Σf
Now, according to given condition
→ N = Σf
→ N = 50
→ N/2 = 50/2 = 25
Cumulative frequency i.e greater than 25 is 36
∴ Median Class = 60 - 80
l = 60
h = 20
f = 12
c.f (preceding class) = 24
→ Me = l + {h × (N/2 - cf/f)}
Substitute all the values
→ Me = 60 + {20 × (25 - 24)/12}
→ Me = 60 + {20 × 1/12}
→ Me = 60 + 20/12
→ Me = 60 + 5/3
→ Me = 60 + 1.66
→ Me = 61.66
Hence,
- Median of given data is 61.66
Note :
Me denotes Median
Σ → Sigma → Summation
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