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Mean, Median and Mode · Question 29 of 67

The monthly electricity consumption of 60 households in a housing society is grouped below.

Question 29

MediumOriginal question
Units consumedNumber of households
60–806
80–10010
100–12020
120–14014
140–16010

The monthly electricity consumption of 60 households in a housing society is grouped below. What is the mode of the consumption?

Options for question 29

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Modal class 100–120: l=100l = 100, f1=20f_1 = 20, f0=10f_0 = 10, f2=14f_2 = 14, h=20h = 20.

  2. Mode = l+f1−f02f1−f0−f2×h=100+1040−24×20l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h = 100 + \frac{10}{40 - 24} \times 20.

  3. =100+1016×20=100+12.5=112.5= 100 + \frac{10}{16} \times 20 = 100 + 12.5 = 112.5 units.

Worth noting

110 units is the class mark of the modal class, not the mode. 106.25 units uses h=10h = 10, and 100 units stops at the lower limit.

Concept
Mode of grouped data by formula
Typical time
70 s
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