Question

Find the mode of the following distribution:

Age in (years)	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	8	14	25	28	25	10	5

Answer 1

Here, the maximum class frequency is 28, and the class corresponding to this frequency is 30-40.
So, the modal class is 30-40
Now, modal class = 30-40,
lower limit (I) of the modal class= 60, class size(h)=10
frequency $$({ f }_{ 1 })$$ of the modal class=28
frequency $$({ f }_{ 0 })$$ of class preceding the modal class=25
frequency $$({ f }_{ 2 })$$ of class preceding the modal class=25
Now, let us substitute these values in the formula
$$Mode = 1+\left( \frac { { f }_{ 1 }-{ f }_{ 0 } }{ 2{ f }_{ 1 }-{ f }_{ 0 }-{ f }_{ 2 } } \right) \times h$$
$$=30+\left( \frac { 28-25 }{ 2\times28-25-25 } \right) \times 10$$
$$=30+\frac { 3 }{ 6 } \times 10$$
$$=30+5$$
$$=35$$