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# The given distribution shows the number of runs scored by some top batsmen of the world in one- day international cricket matches. 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 Find the mode of the data.

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.