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 =4.55

Given:-

petrol filled No of vehical

1 - 3 33

4 -6 40

7 - 9 27

10-12 18

13 -15 12

To find:-

mode

solution:-

here uneven frequency are present

first we convert this in equal frequency

petrol filled No of vehical

0.5 - 3.5 33

3.5 -6.5 40

6.5 - 9.5 27

9.5-12.5 18

12.5 -15.5 12

now,

here the maximum frequency is 40 corresponding to the class interval

3.5 - 6.5

There for the modal class is 3.5 - 6.5

here,

$l_{1} = 3.5 \\ l_{2} = 6.5 \\ f_{1} = 40 \\ f_{0} = 33 \\ f_{2} = 27$

as we know

$mode = l_{1} + \frac{f_{1} - f_{0} }{(f_{1} -f_{0} ) +f_{1} - f_{2} } \times (l_{2} - l_{1} ) \\ \\ mode \: = 3.5 + \frac{40 - 33}{(40 - 33) + (40 - 27)} \times (6.5 - 3.5) \\ \\ mode = 3.5 + \frac{7}{7 + 13} \times 3 \\ \\ mode = 3.5 + \frac{7}{20} \times 3 \\ \\ mode = 3.5 + \frac{21}{20} \\ \\ mode = 3.5 + 1.05 \\ \\ mode = 4.55$