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Run Scored | Number of Batsman |
3000-4000 | 4 |
4000-5000 | 18 |
5000-6000 | 9 |
6000-7000 | 7 |
7000-8000 | 6 |
8000-9000 | 3 |
9000-10000 | 1 |
10000-11000 | 1 |
Answer :
The class 4000-5000 has the maximum frequency , therefore, this is the modal class.
Here l = 4000,
h = 1000,
f1 = 18,
f0 = 4 and
f2 = 9
Now, let us substitute these values in the formula
Mode \(= l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)
\(= \ 4000 \ + \ ( \frac{18 \ - \ 4}{2 \ × \ 18 \ - \ 4 \ - \ 9}) \ × \ 1000 \)
\(= \ 4000 \ + \ \frac{18 \ - \ 4}{36 \ - \ 4 \ - \ 9} \ × \ 1000 \)
\(= \ 4000 \ + \ \frac{14}{23} \ × \ 1000 \)
\(= \ 4000 \ + \ 608.695 \ = 4608.7 \)
\(\therefore \) The mode of the given data is 4608.7 runs.