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A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find mode of the data
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes

Solution:

Modal Class is the class with the highest frequency

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h

Here,

  • Class size, h
  • Lower limit of modal class, l
  • Frequency of modal class, f₁
  • Frequency of class preceding modal class, f₀
  • Frequency of class succeeding the modal class, f₂

From the table, it can be observed that the maximum class frequency is 20, belonging to class interval 40 − 50

Therefore, modal class = 40 − 50

Class size, h = 10

Lower limit of modal class, l = 40

Frequency of modal class, f₁ = 20

Frequency of class preceding modal class, f₀ = 12

Frequency of class succeeding the modal class, f₂ = 11

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂) ]× h

= 40 + [(20 - 12)/(2 × 20 - 12 - 11)] × 10

= 40 + [8/(40 - 23)] × 10

= 40 + (8/17) × 10

= 40 + 4.705

= 44.705

≈ 44.7

Hence, the mode is 44.7

☛ Check: NCERT Solutions for Class 10 Maths Chapter 14

Video Solution:

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find mode of the data.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.2 Question 6

Summary:

The mode of the data showing the number of cars passing through a spot on a road for 100 periods each of 3 minutes is 44.7.

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