Data on the amounts of federal on-budget funds for research programs at universities and related institutions for selected years appear in the table below. What is the standard deviation of the federal on-budget funds for research programs for this period? Round your answer to three decimal places.

A) 10.125
B) 8.000
C) 7.990
D) 11.571
E) 7.474

Question

Data on the amounts of federal on-budget funds for research programs at universities and related institutions for selected years appear in the table below. What is the standard deviation of the federal on-budget funds for research programs for this period? Round your answer to three decimal places.
Data on the amounts of federal on-budget funds for research programs at universities and related institutions for selected years appear in the table below. What is the standard deviation of the federal on-budget funds for research programs for this period? Round your answer to three decimal places. A) 10.125 B) 8.000 C) 7.990 D) 11.571 E) 7.474

A) 10.125 
B) 8.000 
C) 7.990 
D) 11.571 
E) 7.474

Quizplus · Accepted Answer

To find the standard deviation for the given set of data, we can use the formula:
Standard deviation = sqrt[ Σ(xi - x̄)^2 / (n - 1) ]
where Σ is the summation symbol, xi is each value in the dataset, x̄ is the mean of the dataset, and n is the sample size.
Using the data given in the table, we can calculate the mean as:
x̄ = (13.4 + 12.1 + 10.9 + 9.7 + 11.5) / 5 = 11.12
Using this value, we can calculate the standard deviation as:
Standard deviation = sqrt[ ((13.4-11.12)^2 + (12.1-11.12)^2 + (10.9-11.12)^2 + (9.7-11.12)^2 + (11.5-11.12)^2) / (5-1) ]
Standard deviation = sqrt[ 6.698 / 4 ] ≈ 7.990 (rounded to three decimal places)
Therefore, the best choice is C, which is the closest to the calculated value of the standard deviation.

Data on the Amounts of Federal On-Budget Funds for Research