Question

For the data set 6, 5, 10, 11, 13, the mean, x, is 9. What is the standard deviation?

A. 9.2
B. 3.4
C. 3
D. 11.25

Answer 1

The standard deviation of the data set is found by calculating the squared differences from the mean, dividing by the number of data points minus one, and taking the square root of this result, which gives an approximate value of 3.4.

Step-by-step explanation:

To calculate the standard deviation of the data set 6, 5, 10, 11, 13 with a mean of 9, we first need to find the sum of the squared differences from the mean. Here are the steps:

• Subtract the mean from each data point: (6-9), (5-9), (10-9), (11-9), (13-9) giving us -3, -4, 1, 2, 4.
• Square each of these differences: (-3)*2, (-4)*2, 1*2, 2*2, 4*2 giving us 9, 16, 1, 4, 16.
• Add up these squared differences: 9 + 16 + 1 + 4 + 16 = 46.
• Since the sample standard deviation formula is used, divide this sum by the number of data points minus one (n-1), which is 46/(5-1) = 46/4 = 11.5.
• Take the square root of this result to get the standard deviation: √11.5 ≈ 3.4.

Therefore, the standard deviation of this data set is approximately 3.4, which corresponds to option B.