Calculate the variance for the following data: 3, 7, 7, 19. (2022)

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Question: Calculate the variance for the following data: 3, 7, 7, 19. (2022)

Options:

Correct Answer: 25

Exam Year: 2022

Solution:

Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.

Calculate the variance for the following data: 3, 7, 7, 19. (2022)

Calculate the variance for the following data: 3, 7, 7, 19. (2022)

Step 1: Add all the numbers together: 3 + 7 + 7 + 19.
Step 2: Calculate the total: 3 + 7 + 7 + 19 = 36.
Step 3: Count how many numbers there are: There are 4 numbers.
Step 4: Calculate the mean (average) by dividing the total by the count: 36 / 4 = 9.
Step 5: Subtract the mean from each number to find the difference: (3-9), (7-9), (7-9), (19-9).
Step 6: Calculate the differences: -6, -2, -2, 10.
Step 7: Square each difference: (-6)² = 36, (-2)² = 4, (-2)² = 4, (10)² = 100.
Step 8: Add the squared differences together: 36 + 4 + 4 + 100 = 144.
Step 9: Divide the total of squared differences by the count of numbers to find the variance: 144 / 4 = 36.

Mean Calculation – The mean is the average of a set of numbers, calculated by summing the values and dividing by the count.
Variance Calculation – Variance measures the spread of a set of numbers, calculated as the average of the squared differences from the mean.
Population vs Sample Variance – Understanding the difference between calculating variance for a population (using N) versus a sample (using N-1).