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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.

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$

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?

Similar Questions

From the data given below,state which group is more variable,$A$ or $B$?

Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

Group $A$ $9$ $17$ $32$ $33$ $40$ $10$ $9$

Group $B$ $10$ $20$ $30$ $25$ $43$ $15$ $7$

The coefficient of variation for the following data is
Class interval $0-2$ $2-4$ $4-6$ $6-8$ $8-10$
Frequency $2$ $3$ $5$ $3$ $2$

From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$

$Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

$A$ data consists of $n$ observations $x_1, x_2, ......, x_n$. If $\sum_{i=1}^n (x_i + 1)^2 = 9n$ and $\sum_{i=1}^n (x_i - 1)^2 = 5n$,then the standard deviation of this data is

Find the mean and variance for the following frequency distribution:

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

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