High School

Find the range and the coefficient of the range for the following data:

Marks: 20 - 30, 30 - 40, 40 - 50, 50 - 60, 60 - 70, 70 - 80, 80 - 90
No. of Students: 10, 12, 15, 20, 25, 13, 38

Options:
1. 70, 0.54
2. 60, 1.54
3. 70, 0.64
4. 60, 0.64

Answer :

To solve this problem, we need to find the range and the coefficient of the range for the given data.

Step-by-Step Solution

  1. Determine the Range:
    The range of a data set is calculated by subtracting the smallest value in the data set from the largest value.

    From the given data, the smallest mark is from the range $20 - 30[tex], which is $20[/tex], and the largest mark is from the range $80 - 90[tex], which is $90[/tex].

    [tex]\text{Range} = \text{Largest value} - \text{Smallest value} = 90 - 20 = 70[/tex]

  2. Calculate the Coefficient of the Range:
    The coefficient of range is a relative measure of dispersion, given by the formula:

    [tex]\text{Coefficient of Range} = \frac{\text{Range}}{\text{Sum of the Largest and Smallest values}}[/tex]

    Substituting the known values:

    [tex]\text{Coefficient of Range} = \frac{70}{90 + 20} = \frac{70}{110} \approx 0.636[/tex]

  3. Conclusion:
    Based on the calculations:

    • The range of the data is $70$.
    • The coefficient of the range is approximately $0.636[tex]. This rounds to the given option $0.64[/tex].

    Therefore, the correct multiple-choice option is:

    Option 3: 70, 0.64

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