6. 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

The class 40-50 has the maximum frequency, therefore, this is the modal class.

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

Now, let us substitute these values in the formula
Mode \( = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)

\(= \ 40 \ + \ ( \frac{20 \ - \ 12}{40 \ - \ 12 \ - \ 11}) \ × \ 10 \)

\( = \ 40 \ + \ \frac{8}{17} \ × \ 10 \)

\( = \ 40+4.7 \ = \ 44.7 \)

∴ Mode = 44.7 cars