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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.
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.
Solution :
Given: The frequency distribution of runs scored by top batsmen in one-day international cricket matches is as follows:
| Runs Scored | Number of Batsmen ($f_i$) |
|---|---|
| 3000 - 4000 | 4 |
| 4000 - 5000 | 18 |
| 5000 - 6000 | 9 |
| 6000 - 7000 | 7 |
| 7000 - 8000 | 6 |
| 8000 - 9000 | 3 |
| 9000 - 10000 | 1 |
| 10000 - 11000 | 1 |
To Find: The mode of the given grouped frequency distribution.
Step 1: Identify the Modal Class
The modal class is the class interval with the highest frequency. Looking at the table, the highest frequency is $18$, which corresponds to the class interval $4000 - 5000$.
Therefore, the Modal Class is $4000 - 5000$.
Step 2: State the Formula for Mode
The formula for calculating the mode of grouped data 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: Assign Values to Variables
From the distribution:
$l = 4000$
$h = 5000 - 4000 = 1000$
$f_1 = 18$
$f_0 = 4$
$f_2 = 9$
Step 4: Substitute Values into the Formula
$\text{Mode} = 4000 + \left( \frac{18 - 4}{2(18) - 4 - 9} \right) \times 1000$
$\text{Mode} = 4000 + \left( \frac{14}{36 - 13} \right) \times 1000$
$\text{Mode} = 4000 + \left( \frac{14}{23} \right) \times 1000$
$\text{Mode} = 4000 + \frac{14000}{23}$
Step 5: Perform the Arithmetic Calculation
Dividing $14000$ by $23$:
$14000 \div 23 \approx 608.6956...$
Rounding to two decimal places, we get $608.70$.
$\text{Mode} = 4000 + 608.70$
$\text{Mode} = 4608.70$
Final Answer: The mode of the given data is 4608.7 runs.
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.
- Q2: The following data gives the information on the observed lifetimes (in hours) of 225 electrical components : Determine the modal lifetimes of the components.
- 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.
- 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:
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