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Class Interval | Frequency |
0-10 | 5 |
10-20 | x |
20-30 | 20 |
30-40 | 15 |
40-50 | y |
50-60 | 5 |
Total | 60 |
Answer :
Given that median is 28.5 and \(n \ = \ \sum f_i \ = \ 60 \)
Here n = 60
\( \Rightarrow \ \frac{n}{2} \ = \ 30 \)
Since the median is given to be 28.5, thus the median class is 20-30.
\(\therefore \) l = 20, h = 10, f = 20 and cf = 5 + x
\(\therefore \) median \(= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h \)
\(\Rightarrow \ 28.5 \ = \ 20 \ + \ \frac{30 \ - \ 5 \ - \ x}{20} \ × \ 10 \)
\( \Rightarrow \ 57 \ = \ 40 \ + \ 25 \ - \ x \)
\( \Rightarrow \ x \ = \ 65 \ - \ 57 \ \)
\(\Rightarrow \ x \ = \ 8 \)
Also, 45 + x + y = 60
[ As n = 60 ]
\(\Rightarrow \ 45 \ + \ 8 \ + \ y \ = \ 60 \)
\(\Rightarrow \ y \ = \ 60 \ - \ 53 \ \)
\( \Rightarrow \ y \ = \ 7 \)
\(\therefore \) x = 8, y = 7