A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :

Number of cars	Frequency
0 - 10	7
10 - 20	14
20 - 30	13
30 - 40	12
40 - 50	20
50 - 60	11
60 - 70	15
70 - 80	8

By formula,

Mode = l + $\Big(\dfrac{f$1 - f0}{2f1 - f0 - f_2}\Big) \times h

Here,

1. Class size is h.

2. The lower limit of modal class is l

3. The Frequency of modal class is f₁.

4. Frequency of class preceding modal class is f₀.

5. Frequency of class succeeding the modal class is f₂.

Class 40 - 50 has the highest frequency.

∴ It is the modal class.

∴ l = 40, f₁ = 20, f₀ = 12, f₂ = 11 and h = 10.

Substituting values we get :

$\text{Mode} = 40 + \Big(\dfrac{20 - 12}{2 \times 20 - 12 - 11}\Big) \times 10 \\[1em] = 40 + \dfrac{8}{40 - 23} \times 10 \\[1em] = 40 + \dfrac{80}{17} \\[1em] = 40 + 4.7 \\[1em] = 44.7$

Hence, mode = 44.7 cars.