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
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.
☛ Related Questions:
- The following data gives information on the observed lifetimes (in hours) of 225 electric components. Determine the modal lifetimes of the components.
- The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also find the mean monthly expenditure.
- The following data gives the state-wise, teacher student ratio in higher secondary schools of India. Find the mode and mean of the data and interpret the two.
- The given distribution shows the number of runs scored by some top batsman of the world in one-day international cricket matches. Find the mode of the data.