Question

true of false the first distribution shown below has a smaller standard deviation than does the second distribution. 11,12,13,14,15,16,17,18,19,20,21,22,111,112,113,114,115,116,117,118,119,120,121,122

Answer 1

Answer:

False

Step-by-step explanation:

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

$Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}}$

where, $\bar{x}$ is mean of the distribution.

Here, First distribution is 11,12,13,14,15,16,17,18,19,20,21,22

and Second distribution is 111,112,113,114,115,116,117,118,119,120,121,122

The mean of first distribution is 16.5

and mean of second distribution is 116.5

So the standard deviation of first distribution is 3.605

and the standard deviation of second distribution is 3.605

Hence, standard deviation is same for both distribution.

Answer 2

false becasue 11,12,13,14,15,16,17,18,19,20,21, and 22 is bigger and 111,112,113,114,115,116,117,118,119,120,121, and 122 is smaller.