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(D) Let the original marks be $x_i$ and the new marks be $y_i = x_i + 10$.Measures of central tendency like mean,median,and mode are affected by a cha

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variance

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(D) Let the original marks be $x_i$ and the new marks be $y_i = x_i + 10$.Measures of central tendency like mean,median,and mode are affected by a change of origin (adding a constant).Specifically,if each observation is increased by a constant $c$,the mean,median,and mode also increase by $c$.However,measures of dispersion like variance and standard deviation are independent of the change of origin.Variance is defined as $\sigma^2 = \frac{1}{n} \sum (x_i - \overline{x})^2$.For the new marks $y_i$,the variance is $\sigma_y^2 = \frac{1}{n} \sum (y_i - \overline{y})^2 = \frac{1}{n} \sum ((x_i + 10) - (\overline{x} + 10))^2 = \frac{1}{n} \sum (x_i - \overline{x})^2 = \sigma_x^2$.Thus,the variance remains unchanged.

	Section $A$	Section $B$
Number of students	$50$	$60$
Average marks in the test	$45$	$45$
Variance of distribution of marks	$64$	$81$

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

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