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Q2:
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Determine the modal lifetimes of the components.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Determine the modal lifetimes of the components.
Solution :
Given: The frequency distribution of the lifetimes (in hours) of 225 electrical components is as follows:
| Lifetimes (hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
|---|---|---|---|---|---|---|
| Frequency ($f_i$) | 10 | 35 | 52 | 61 | 38 | 29 |
To Find: The modal lifetime of the electrical components.
Step 1: Identifying the Modal Class
The modal class is the class interval with the highest frequency. Looking at the frequency distribution table, the highest frequency is $61$, which corresponds to the class interval $60-80$.
Therefore, the Modal Class is $60-80$.
Step 2: Stating the Formula for Mode
The formula for calculating the mode of a grouped frequency distribution is:
$\text{Mode} = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$
Where:
$l$ = Lower limit of the modal class
$h$ = Size of the class interval
$f_1$ = Frequency of the modal class
$f_0$ = Frequency of the class preceding the modal class
$f_2$ = Frequency of the class succeeding the modal class
Step 3: Extracting the Values
From the given data:
$l = 60$
$h = 80 - 60 = 20$
$f_1 = 61$
$f_0 = 52$
$f_2 = 38$
Step 4: Substituting Values into the Formula
$\text{Mode} = 60 + \left( \frac{61 - 52}{2(61) - 52 - 38} \right) \times 20$
[Substituting the identified values into the formula]
Step 5: Performing the Arithmetic Calculations
$\text{Mode} = 60 + \left( \frac{9}{122 - 90} \right) \times 20$
$\text{Mode} = 60 + \left( \frac{9}{32} \right) \times 20$
$\text{Mode} = 60 + \left( \frac{180}{32} \right)$
$\text{Mode} = 60 + 5.625$
$\text{Mode} = 65.625$
Final Answer: The modal lifetime of the electrical components is 65.625 hours.
More Questions from Class 10 Mathematics Statistics EXERCISE 13.2
- Q1: The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
- Q3: 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 :
- Q4: The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
- Q5: The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the data.
- Q6: 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 the mode of the data:
CBSE Solutions for Class 10 Mathematics Statistics
Chapters in CBSE - Class 10 Mathematics
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