If the data set is: 5, 7, 9, 11, what is the variance? (2022)

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Question: If the data set is: 5, 7, 9, 11, what is the variance? (2022)

Options:

Correct Answer: 2

Exam Year: 2022

Solution:

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 5.

If the data set is: 5, 7, 9, 11, what is the variance? (2022)

If the data set is: 5, 7, 9, 11, what is the variance? (2022)

Step 1: Add all the numbers in the data set: 5 + 7 + 9 + 11.
Step 2: Calculate the total: 5 + 7 + 9 + 11 = 32.
Step 3: Count how many numbers are in the data set: There are 4 numbers.
Step 4: Calculate the mean (average) by dividing the total by the count: 32 / 4 = 8.
Step 5: Subtract the mean from each number in the data set: (5-8), (7-8), (9-8), (11-8).
Step 6: Calculate the results of the subtractions: -3, -1, 1, 3.
Step 7: Square each of the results: (-3)² = 9, (-1)² = 1, (1)² = 1, (3)² = 9.
Step 8: Add the squared results together: 9 + 1 + 1 + 9 = 20.
Step 9: Divide the total of the squared results by the count of numbers: 20 / 4 = 5.
Step 10: The variance of the data set is 5.

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.