For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

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Question: For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

Options:

Correct Answer: 6

Exam Year: 2023

Solution:

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6. Variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²] / 5 = 8.

For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

Step 1: Add all the numbers in the data set: 2 + 4 + 6 + 8 + 10.
Step 2: Count how many numbers are in the data set. There are 5 numbers.
Step 3: Divide the total from Step 1 by the count from Step 2 to find the mean: (2 + 4 + 6 + 8 + 10) / 5.
Step 4: Calculate the mean, which is 6.
Step 5: Subtract the mean from each number in the data set: (2-6), (4-6), (6-6), (8-6), (10-6).
Step 6: Square each of the results from Step 5: (2-6)², (4-6)², (6-6)², (8-6)², (10-6)².
Step 7: Add all the squared results together.
Step 8: Divide the total from Step 7 by the count of numbers (5) to find the variance.

Mean Calculation – The mean is calculated by summing all data points and dividing by the number of points.
Variance Calculation – Variance measures the spread of data points from the mean, calculated as the average of the squared differences from the mean.