Question

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

The mode of the volume is 4.55

Class             Frequency

0.5-3.5                 33

3.5-6.5                 40

6.5-9.5                 27

9.5-12.5                18

12.5.5-15.5            12

---------------------------------

Total                    130

Maximum Frequency = 40

Modal class is 3.5-6.5

Mode = $l + (\frac{f_{1}- f_{0}  }{2f_{1}-f_{0}-f_{2}} )C$

l = lower boundary of modal class = 3.5

$f_{1}$ =   frequency of modal class = 40

$f_{0}$ = frequency of preceding class = 33

$f_{2}$ = frequency of succeeding class = 27

C = class length of the modal class = 3

Mode = $3.5 + (\frac{40-33}{2(40)-33-27} )3$

          = $3.5 + (\frac{7}{20})3$

          = 3.5 + 1.05

          = 4.55