Find the variance and the standard deviation (correct to two decimal places) of the following data set. $20,21,22,23,24$
A) variance: $2$ standard deviation: $1.41$
B) variance: $2$ standard deviation: $22$
C) variance: $1.41$ standard deviation: $2$
D) variance: $4$ standard deviation: $1.41$
E) variance: $22$ standard deviation: $1.41$

Question

Quizplus · Accepted Answer

To find the variance, we first need to find the mean: 
Mean = (20+21+22+23+24)/5 = 22 
Then, we need to find the difference between each value and the mean:

Value | Difference from Mean | Squared Difference 
20      -2                   4 
21      -1                   1 
22       0                    0 
23       1                   1 
24       2                   4

To find the variance, we take the average of the squared differences:

Variance = (4+1+0+1+4)/5 = 2

To find the standard deviation, we take the square root of the variance:

Standard deviation = sqrt(2) = 1.41 (rounded to two decimal places)

Therefore, the best choice is A.

Find the Variance and the Standard Deviation (Correct to Two 20,21,22,23,2420,21,22,23,2420,21,22,23,24

Find the Variance and the Standard Deviation (Correct to Two $20,21,22,23,24$