What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?
Practice Questions
Q1
What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?
5.5
4.5
6.5
3.5
Questions & Step-by-Step Solutions
What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?
Step 1: Find the mean (average) of the data set. Add all the numbers together: 10 + 12 + 23 + 23 + 16 + 23 + 21 = 138. Then divide by the number of values (7): 138 / 7 = 19.14.
Step 2: Find the variance. Subtract the mean from each number to find the difference: (10 - 19.14), (12 - 19.14), (23 - 19.14), (23 - 19.14), (16 - 19.14), (23 - 19.14), (21 - 19.14). This gives you: -9.14, -7.14, 3.86, 3.86, -3.14, 3.86, 1.86.
Step 3: Square each of these differences: (-9.14)^2, (-7.14)^2, (3.86)^2, (3.86)^2, (-3.14)^2, (3.86)^2, (1.86)^2. This results in: 83.58, 50.98, 14.82, 14.82, 9.86, 14.82, 3.46.
