Question

Formula used to find the class-mark of a class interval is

• A. Class mark = \( \frac{\text{Upper limit + lower limit}}{2} \)
• B. Class mark = \( \frac{\text{Upper limit - lower limit}}{2} \)
• C. Class mark = \( \frac{\text{Upper limit} \times \text{lower limit}}{2} \)
• D. Class mark = \( \frac{\text{Upper limit} \div \text{lower limit}}{2} \) % OCR seems to have "Upperlimit+lowerlimit / 2" for option 4 again

Hint:

- Class Interval: A range into which data is grouped (e.g., 10-20). It has a lower limit (10) and an upper limit (20). - Class Mark (Midpoint): The central value of a class interval. Formula: \( \text{Class Mark} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2} \). - Class Size/Width: Upper Class Limit - Lower Class Limit.

Answer 1

The Correct Option is A

Step 1: Understand the definition of a class mark.
In statistics, for a grouped frequency distribution, a class interval has a lower limit and an upper limit.
The class mark (or midpoint) of a class interval is the value that represents the center of that interval.
It is used in calculations like finding the mean of grouped data.

Step 2: Recall the formula for the class mark.
The class mark is calculated as the average of the upper and lower limits of the class interval.
\[ \text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \] Or, equivalently, \[ \text{Class mark} = \frac{\text{Upper limit} + \text{Lower limit}}{2} \]
Step 3: Compare with the given options.
Option (1) matches this formula.
Option (2) represents half the class size or range, not the midpoint.
Options (3) and (4) are incorrect operations for finding a midpoint.
(The OCR for option (4) in the Telugu part shows Upperlimit+lowerlimit / 2 which is same as (1).
However, English option shows division, which is clearly wrong).
Assuming the English options are to be followed, option (1) is correct.