Question 6

We will use the formula for the mode of grouped data.

Step 1 — Identify modal class and values

First, we find the highest frequency. The highest frequency in the table is 20. This frequency corresponds to the class interval 40 - 50. So, the modal class is 40 - 50. The lower limit of the modal class ($l$) is 40. The frequency of the modal class ($f_1$) is 20. The frequency of the class preceding the modal class ($f_0$) is 12. The frequency of the class succeeding the modal class ($f_2$) is 11. The class size ($h$) is $10 - 0 = \textbf{10}$.

$\boxed{\text{Modal class} = 40 - 50}$

Step 2 — Calculate the mode

Now, we use the mode formula for grouped data. The formula is $Mode = l + \left[ \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \right] \times h$. Let's substitute the values we found.

$Mode = 40 + \left[ \frac{(20 - 12)}{(2 \times 20 - 12 - 11)} \right] \times 10$

$= 40 + \left[ \frac{8}{(40 - 12 - 11)} \right] \times 10$

$= 40 + \left[ \frac{8}{(28 - 11)} \right] \times 10$

$= 40 + \left[ \frac{8}{17} \right] \times 10$

$= 40 + \frac{80}{17}$

$= 40 + 4.7058...$

$= 44.7 \text{ (rounded to one decimal place)}$

$\boxed{44.7 \text{ cars}}$

Answer

(i) The mode of this data is 44.7 cars.