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  4. Find the mode from the data given below: <table class=table table-bordered > Marks obtained 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 No. of students 18 20 25 30 16 14

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Q. Find the mode from the data given below:
Marks obtained 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30
No. of students 18 20 25 30 16 14

Statistics

Solution:

30 is greatest number in given table
$\therefore $ mode group = $15 - 20$
$\therefore \:\:\: l_1$(lower limit) = $15, f = 30, f_{1} = 25,f_{2} = 16, i = 20 - 15 = 5$
We know that,
mode = $l_1 + \frac{f - f_{1}}{2f - f_{1} - f_{2}} \times i $
$ = 15 + \frac{30 - 25}{2 \times 30 - 25 - 16} \times 5$
$ = 15 + \frac{5}{60 - 41} \times 5 = 15 + \frac{25}{19} = 16.3$