If the standard deviation of $3, 8, 6, 10, 12, 9, 11, 10, 12, 7$ is $2.71$ , then the standard deviation of $30, 80, 60, 100, 120, 90, 110, 100, 120, 70$ is

$2.71$
$27.1$
$(2.71) \sqrt{10}$
$(2.71) \sqrt{2}$
$0.271$

Open in App

Solution

The correct option is B
$27.1$

Explanation for the correct option:
Given: The standard deviation of $3, 8, 6, 10, 12, 9, 11, 10, 12, 7$ is $2.71$ ,
We know that the standard deviation is dependent on the scale.
If the values in the sample are multiplied by $k,$ then the standard deviation will be $k$ times.
In the required sample, samples are multiplied by $10$ .
Therefore, standard deviation $= 10 \times 2.71$
standard deviation $= 27.1$
Hence option(B) is the correct option.

Suggest Corrections

Similar questions

Find the mean, variance and standard deviation using short-cut method

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	12	13	10	8

Class	50-60	60-70	70-80	80-90	90-100
Frequency	8	6	12	11	p

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

10, 11, 12, . . . ., 19

Class interval	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Frequency	$3$	$7$	$12$	$15$	$8$	$3$	$2$

Join BYJU'S Learning Program