JEE Mathematics 2024 Question with Solution

Step-by-step solution

Common mistakes

• Using the simple mean of the listed $x_i$ values instead of the frequency-weighted mean is incorrect because each value occurs $f_i$ times. First compute $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$, then use it in the variance formula.

• Dividing by the number of distinct values $7$ instead of the total frequency $\sum f_i$ gives the wrong variance. In a discrete frequency distribution, each frequency counts as repeated observations, so the denominator must be the total number of observations.

• Computing variance as $\frac{\sum f_i (x_i-\bar{x})}{\sum f_i}$ is wrong because variance uses squared deviations. The correct expression is $\sigma^2 = \frac{\sum f_i (x_i-\bar{x})^2}{\sum f_i}$.