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

The mode  of the volume = 4.56

Step-by-step explanation:

The given table:

Petrol filled (litre)  1-3    4-6    7-9     10-12    13-15

No. of vehicles     33      40    27       18          12​

To find, the mode  of the volume = ?

As the class 4 - 6 has maximum frequency, so it is the modal class.

∴ $x_{k}=4,f_{k}=40,f_{k-1}=33,f_{k+1}=27$ and $h=2$

We know that,

Mode $=x_{k} +\dfrac{f_{k}-f_{k-1}}{2f_{k}-f_{k-1}-f_{k+1}}\times h$

$=4 +\dfrac{40-33}{2(40)-33-22}\times 2$

$=4 +\dfrac{7}{80-55}\times 2$

$=4 +\dfrac{14}{25}$

$=4 +0.56$

= 4.56

Hence, the mode  of the volume = 4.56