Question

What is the standard deviation of the data set (rounded to the nearest tenth): 3, 17, 18, 15, 12, 21, 9?

a) 6.0
b) 5.8
c) 5.7
d) 6.1

Answer 1

To find the standard deviation of a data set, we can use the formula. The given data set has a standard deviation of approximately 5.6 (rounded to the nearest tenth).

Step-by-step explanation:

To find the standard deviation of a data set, we can use the formula:

Step 1: Find the mean of the data set.

Step 2: Subtract the mean from each data point and square the result.

Step 3: Find the mean of the squared differences.

Step 4: Take the square root of the mean of the squared differences.

Let's apply these steps to the given data set:

Step 1: Mean = (3 + 17 + 18 + 15 + 12 + 21 + 9) / 7 = 95 / 7 ≈ 13.6

Step 2: (3 - 13.6)² + (17 - 13.6)² + (18 - 13.6)² + (15 - 13.6)² + (12 - 13.6)² + (21 - 13.6)² + (9 - 13.6)² ≈ 218.4

Step 3: 218.4 / 7 ≈ 31.2

Step 4: Square root of 31.2 ≈ 5.6

Therefore, the standard deviation of the data set is approximately 5.6 (rounded to the nearest tenth).