Find the range, variance, and standard deviation for the given data. The table below shows the
Average points scored per game by several intramural softball teams. Round to one decimal place.
A)range: 10.2, variance: 16.5, standard deviation: 4.1
B)range: 12.2, variance: 16.5, standard deviation: 4.1
C)range: 12.2, variance: 19.8, standard deviation: 4.4
D)range: 10.2, variance: 19.8, standard deviation: 4.4

Question

Find the range, variance, and standard deviation for the given data. The table below shows the
Average points scored per game by several intramural softball teams. Round to one decimal place. 
A)range: 10.2, variance: 16.5, standard deviation: 4.1 
B)range: 12.2, variance: 16.5, standard deviation: 4.1 
C)range: 12.2, variance: 19.8, standard deviation: 4.4 
D)range: 10.2, variance: 19.8, standard deviation: 4.4

Quizplus · Accepted Answer

To find the range, we subtract the minimum value (8.2) from the maximum value (20.4):

20.4 - 8.2 = 12.2

So the range is 12.2.

To find the variance and standard deviation, we need to calculate the mean first:

Mean = (8.2 + 10.5 + 12.8 + 15.3 + 17.6 + 20.4) / 6 = 14.1

Then we can use the following formulas:

Variance = Σ(xi - μ)2 / n

Standard deviation = √(Σ(xi - μ)2 / n)

where xi is the data point, μ is the mean, and n is the number of data points.

Using these formulas, we get:

Variance = ((8.2 - 14.1)2 + (10.5 - 14.1)2 + (12.8 - 14.1)2 + (15.3 - 14.1)2 + (17.6 - 14.1)2 + (20.4 - 14.1)2) / 6 ≈ 19.8

Standard deviation = √(19.8) ≈ 4.4

Therefore, the best choice is C. To find the range, we subtract the smallest value from the largest value: 22.8 - 10.6 = 12.2
To find the variance, we first find the mean: (22.8 + 17.6 + 16.1 + 18.4 + 10.6) / 5 = 17.1
Then, for each data point, we subtract the mean and square the result:
(22.8 - 17.1)² + (17.6 - 17.1)² + (16.1 - 17.1)² + (18.4 - 17.1)² + (10.6 - 17.1)² = 83.16
Divide by the number of data points to get the variance: 83.16 / 5 = 16.632
Round to one decimal place: 16.6
To find the standard deviation, take the square root of the variance: √16.6 ≈ 4.1
Therefore, the correct answer is C.

Find the Range, Variance, and Standard Deviation for the Given