Question

The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity:

Class (Petrol filled in Liters)	Frequency (Number of Vehicles)
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

Activity:

From the given table,

Modal class = `square`

∴ Mode = `square + [(f_1 - f_0)/(2f_1 -f_0 - square)] xx h`

∴ Mode = `3.5 + [(40 - 33)/(2(40) - 33 - 27)] xx square`

∴ Mode = `3.5 +[7/(80 - 60)] xx 3`

∴ Mode = `square`

∴ The mode of the volume of petrol filled is `square`.

Answer 1

From the given table,

Modal class = 3.5 − 6.5    ...(∵ This class has max. frequency)

∴ Mode = l + `[(f_1 - f_0)/(2f_1 - f_0 - bbunderline(f_2))] xx h`

l = Lower class boundary of the modal class

f₁ = 40 (Frequency of modal class)

f₂ = 27 (Frequency of the class succeding the modal class)

f₀ = 33 (frequency of the class preceding the modal class)

∴ Mode = `3.5 + [(40-33)/(2(40)-33-27)] xx bbunderline3`

∴ Mode = `3.5 +[7/(80-60)] xx3`

∴ Mode = 4.55

∴ The mode of the volume of petrol filled is 4.55.