Grouped frequency distribution? a. None of these b. Class width = \frac{Highest value – lowest value}{sum of frequencies} c. Class width = \frac{Highest value + lowest value}{number of intervals} d. Class width = \frac{Highest value – lowest value}{number of intervals}
What is the formula to find the class width(or class interval) in the grouped frequency distribution? a. None of these b. Class width = \frac{Highest value – lowest value}{sum of frequencies} c. Class width = \frac{Highest value + lowest value}{number of intervals} d. Class width = \frac{Highest value – lowest value}{number of intervals}
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The Correct Answer and Explanation is:
The correct formula for determining the class width in a grouped frequency distribution is:
Class width = (Highest value – Lowest value) / Number of intervals
Therefore, the correct answer is option d.
Explanation:
A grouped frequency distribution organizes data into classes or intervals rather than presenting individual values. To construct this distribution, we must determine the class width, which represents the numerical range of each interval.
Step 1: Understanding Class Width Class width ensures that all data points are divided evenly among the chosen intervals. A higher class width leads to fewer intervals, making the distribution broader, while a lower class width creates more intervals, resulting in a detailed breakdown of the dataset.
Step 2: Formula Justification To find the class width, we subtract the lowest value from the highest value, which gives the total range of the dataset. Dividing this range by the number of intervals ensures that the data is evenly spread across the chosen classes.
Incorrect options:
- Option b, which divides by the sum of frequencies, is incorrect because the class width depends on the range of values rather than frequency count.
- Option c incorrectly adds the highest and lowest values, which does not represent the range of the data.
Step 3: Practical Example Consider a dataset ranging from 10 to 90 with 8 intervals. Using the correct formula:
Class width = (90 – 10) / 8 Class width = 80 / 8 Class width = 10
Each interval will be 10 units wide, allowing the grouped frequency distribution to be constructed accurately.
Grouping data effectively improves analysis and allows patterns to be easily observed. By correctly applying the formula, one ensures a structured representation of statistical data.
