What is the formula to find the class mark of a class interval?

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Points to Remember:

  • Class mark represents the midpoint of a class interval.
  • It’s crucial for calculating various statistical measures.
  • The formula is straightforward and easy to apply.

Introduction:

In statistics, data is often organized into class intervals, especially when dealing with large datasets. A class interval represents a range of values. For example, in a dataset of student ages, we might have class intervals like 10-14, 15-19, 20-24, etc. To simplify calculations and analysis, we often use the class mark (or midpoint) of each interval. The class mark is a representative value for the entire class interval and is used in various statistical calculations like calculating the mean, median, and mode for grouped data.

Body:

Calculating the Class Mark:

The class mark is simply the average of the lower and upper limits of a class interval. The formula is:

Class Mark = (Lower Limit + Upper Limit) / 2

Let’s illustrate with examples:

  • Example 1: Consider the class interval 10-14.

    • Lower Limit = 10
    • Upper Limit = 14
    • Class Mark = (10 + 14) / 2 = 12

  • Example 2: Consider the class interval 25-30.

    • Lower Limit = 25
    • Upper Limit = 30
    • Class Mark = (25 + 30) / 2 = 27.5

  • Example 3: Consider a class interval with unequal class sizes, for instance, 10-15 and 16-25. The formula remains the same:

    • For 10-15: Class Mark = (10+15)/2 = 12.5
    • For 16-25: Class Mark = (16+25)/2 = 20.5

Significance of Class Marks:

Class marks are essential for various statistical computations involving grouped data. They are used to:

  • Calculate the mean of grouped data: The mean is calculated by multiplying each class mark by its frequency, summing these products, and dividing by the total frequency.
  • Represent the class interval graphically: Class marks are used as the x-axis values when representing grouped data using histograms or frequency polygons.
  • Simplify calculations: Using class marks simplifies calculations compared to working with the entire range of values within each interval.

Conclusion:

The formula for calculating the class mark of a class interval is straightforward: (Lower Limit + Upper Limit) / 2. This simple calculation provides a representative value for the entire interval, significantly simplifying statistical analysis of grouped data. Class marks are indispensable for calculating the mean of grouped data and for graphical representation of frequency distributions. Understanding and correctly applying this formula is fundamental to mastering basic statistical concepts and techniques. The use of class marks ensures efficiency and accuracy in statistical analysis, promoting a more robust understanding of data.

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