Question

The following sets of scores all have the same range. Which set has the smallest standard deviation?

a) 4, 4, 4, 16, 16, 16
b) 4, 10, 10, 10, 10, 16
c) 4, 6, 9, 11, 14, 16
d) 4, 8, 10, 12, 16

Answer 1

The set with the smallest standard deviation is option b) 4, 10, 10, 10, 10, 16.

Step-by-step explanation:

The set with the smallest standard deviation is option b) 4, 10, 10, 10, 10, 16.

To find the standard deviation, we need to calculate the mean of the set first. The mean for option b) is (4+10+10+10+10+16)/6 = 60/6 = 10. Then, for each number in the set, subtract the mean and square the result. Sum up all the squared differences and divide by the total number of scores (6) to get the variance. The variance for option b) is [(4-10)^2 + (10-10)^2 + (10-10)^2 + (10-10)^2 + (10-10)^2 + (16-10)^2]/6 = 36/6 = 6.

Finally, take the square root of the variance to get the standard deviation. The standard deviation for option b) is √6 ≈ 2.45. Since option b) has the smallest standard deviation among the given sets, it is the answer.