What is the standard deviation of the set {2, 4, 6, 8, 10}?

What is the standard deviation of the set {2, 4, 6, 8, 10}?

• A. 1.41
• B. 2.00
• C. 2.83
• D. 3.16

Answer: (C)

To determine the standard deviation of the set {2, 4, 6, 8, 10}, we can follow a systematic approach. First, find the mean (average) of the data set. The mean is calculated by summing all the values and dividing by the number of values. The sum of the numbers is: 2 + 4 + 6 + 8 + 10 = 30. Since there are 5 numbers in the set: Mean = 30 / 5 = 6. Next, we find the variance, which involves calculating the squared differences from the mean. For each value, subtract the mean and then square the result: - For 2: (2 - 6)² = (-4)² = 16 - For 4: (4 - 6)² = (-2)² = 4 - For 6: (6 - 6)² = (0)² = 0 - For 8: (8 - 6)² = (2)² = 4 - For 10: (10 - 6)² = (4)² = 16 Now, add these squared differences:

To determine the standard deviation of the set {2, 4, 6, 8, 10}, we can follow a systematic approach.

First, find the mean (average) of the data set. The mean is calculated by summing all the values and dividing by the number of values.

The sum of the numbers is:

2 + 4 + 6 + 8 + 10 = 30.

Since there are 5 numbers in the set:

Mean = 30 / 5 = 6.

Next, we find the variance, which involves calculating the squared differences from the mean. For each value, subtract the mean and then square the result:

• For 2: (2 - 6)² = (-4)² = 16

• For 4: (4 - 6)² = (-2)² = 4

• For 6: (6 - 6)² = (0)² = 0

• For 8: (8 - 6)² = (2)² = 4

• For 10: (10 - 6)² = (4)² = 16

Now, add these squared differences: