If the standard deviation of 0, 1, 2, 3, dots | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The standard deviation of a set of observations is independent of the change of origin.Let the first sequence be $x_i = \{0, 1, 2, \dots, 9\}$ wit

Vedclass · Accepted Answer

$K$

Vedclass · Answer

(A) The standard deviation of a set of observations is independent of the change of origin.Let the first sequence be $x_i = \{0, 1, 2, \dots, 9\}$ with standard deviation $K$.The second sequence is $y_i = \{10, 11, 12, \dots, 19\}$,which can be written as $y_i = x_i + 10$.Since the standard deviation is invariant under the addition of a constant to each observation,the standard deviation of $y_i$ is equal to the standard deviation of $x_i$.Therefore,the standard deviation of the second sequence is also $K$.

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequencies	$5$	$8$	$15$	$16$	$6$

If the standard deviation of $0, 1, 2, 3, \dots, 9$ is $K$,then the standard deviation of $10, 11, 12, 13, \dots, 19$ is

Similar Questions

Find the mean and variance for the following frequency distribution.

Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequencies $5$ $8$ $15$ $16$ $6$

Which of the following data sets has the minimum variance?

The arithmetic mean of marks in Mathematics for four divisions $A, B, C$ and $D$ were $80, 75, 70$ and $72$ respectively. Their standard deviations were $12, 6, 8$ and $10$ respectively. Then,which division has more uniformity?

All students in a classroom performed poorly in mathematics. The teacher decided to increase the marks of each student by $10$. Which of the following statistical measures will not change even after adding the extra marks?

The variance of the data $2, 3, 5, 11, 13, 17, 19$ is nearly

Vedclass Test Series

Exam Paper Generator

Online Exam Module