Frequency Distributions

Concept: In a frequency distribution, for any class interval:
Let be the lower class limit.
Let be the upper class limit.
The mid-point ( ) of the class interval is the average of the lower and upper class limits. Mid-point formula: Step 1: Use the mid-point formula We are given the mid-point formula: We are given (lower class limit) and (mid-point), and we need to find (upper class limit). Step 2: Rearrange the formula to solve for Multiply both sides of the equation by 2: Now, isolate by subtracting from both sides: So, the upper class limit is equal to . Step 3: Compare with the options The derived expression for the upper class limit is . This matches option (3). Example: Let a class interval be 10-20. Lower class limit, . Upper class limit, . Mid-point, . Now let's use the formula to check: . This is correct.