Question

3) The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. Find the mode of the volume. Petrol filled (litre) 1-3 4-6 7-9 10-12 13-15 No. of vehicles 33 40 27 18 12​

Answer 1

Answer:

Mode of volume of petrol =4.55 litres

Step-by-step explanation:

The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. Find the mode of the volume

petrol filled--true class limit--freq

1-3________0.5-3.5_________33->fo

4-6_______ 3.5-6.5_________40->f1

7-9_______ 6.5-9.5_________27->f2

10-12_____9.5-12.5__________18

13-15______12.5-15.5_________12

We know that modal class is that class which have higher frequency,so

Modal class= 3.5-6.5

$Mode = l + \bigg(\frac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg)h$

here

$l = 3.5 \\ f_1 = 40 \\ f_0 =33 \\ f_2 =27 \\ h = 3$

place all values in the formula

$Mode = 3.5+ \bigg(\frac{40 - 33}{2 \times 40 - 33 - 27} \bigg)3 \\ \\ = 3.5 + \bigg(\frac{7}{ 80 - 33 - 27} \bigg)3 \\ \\ = 3.5 + \frac{7}{20} \times 3 \\ \\ = 3.5 + \frac{21}{20} \\ \\ = 3.5 + 1.05 \\ \\ Mode= 4.55$

Hope it helps you.