Find the approximate value of mode for the following data $:$

Marks
$50 - 60$
$60 - 70$
$70 - 80$
$80 - 90$
$90 - 100$
Students
$12$
$10$
$24$
$5$
$9$

71

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72

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73

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74

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Solution

The correct option is D $74$
Here the frequency of class interval $70 - 80$ is the maximum.
So, it is the modal class
Now
$l$ = lower limit of modal class $= 70$
$f_{1} =$ frequency of modal class $= 24$
$f_{0} =$ frequency of class preceding the modal class $= 10$
$f_{2} =$ frequency of class succeeding the modal class $= 5$
$h =$ class interval width $= 10$

Mode $= l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$
$= 70 + (\frac{24 - 10}{2 \times 24 - 10 - 5}) \times 10$
$= 70 + (\frac{14}{48 - 15}) \times 10$
$= 70 + 4.24$
$= 74.24$
Mode $\approx 74$

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