Find the range and the standard deviation.
Where necessary, the choices are rounded to the nearest hundredth.

0, 2, 2, 6, 7, 10, 12, 19

C)
D)
E)

Question

Find the range and the standard deviation. ​
Where necessary, the choices are rounded to the nearest hundredth.
​
0, 2, 2, 6, 7, 10, 12, 19
​
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The range is the difference between the highest and the lowest value in the set. In this case, the highest value is 19 and the lowest value is 0, so the range is 19-0 = 19.

To find the standard deviation, we first need to find the mean. We can do this by adding up all the values and then dividing by the number of values:

(0 + 2 + 2 + 6 + 7 + 10 + 12 + 19) / 8 = 58 / 8 = 7.25

Now we can find the variance, which is the average of the squared differences between each value and the mean:

((0-7.25)^2 + (2-7.25)^2 + (2-7.25)^2 + (6-7.25)^2 + (7-7.25)^2 + (10-7.25)^2 + (12-7.25)^2 + (19-7.25)^2) / 8 
= (53.0625 + 29.0625 + 29.0625 + 1.5625 + 0.0625 + 6.5625 + 19.5625 + 135.0625) / 8 
= 49.125

Finally, we can find the standard deviation by taking the square root of the variance:

√49.125 ≈ 7.01

Therefore, the range is 19 and the standard deviation is approximately 7.01. The best choice that matches these values is B.

Find the Range and the Standard Deviation. ​

Find the Range and the Standard Deviation.