NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.2

Question 2

Step 1: Recall the formula for mean using the assumed mean method:

\[ \bar{x} = a + \dfrac{\sum f_i d_i}{\sum f_i} \]

• \(a\) = assumed mean
• \(f_i\) = frequency of the \(i^{th}\) class
• \(d_i = x_i - a\), where \(x_i\) is the midpoint of the \(i^{th}\) class

Step 2: The formula only needs us to pick an assumed mean (\(a\)) — this can be any number that makes the calculation easy.

Step 3: In practice, we usually choose \(a\) from one of the class midpoints because:

• It is close to the actual mean.
• It makes the subtraction \(x_i - a\) simpler.

Step 4: However, it is not compulsory to take \(a\) as a midpoint. We could assume any convenient number.

Final Step: Since the question says \(a\) must be a midpoint, this statement is false. The correct idea is that \(a\) can be any convenient value, though a midpoint is often chosen for simplicity.