For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

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Question: For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

Options:

Correct Answer: 1.5

Exam Year: 2022

Solution:

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

Step 1: Add all the numbers in the data set: 1 + 2 + 3 + 4 + 5.
Step 2: Calculate the total: 1 + 2 + 3 + 4 + 5 = 15.
Step 3: Count how many numbers are in the data set: There are 5 numbers.
Step 4: Calculate the mean (average) by dividing the total by the count: 15 / 5 = 3.
Step 5: Find the difference between each number and the mean: (1-3), (2-3), (3-3), (4-3), (5-3).
Step 6: Calculate these differences: -2, -1, 0, 1, 2.
Step 7: Square each of these differences: (-2)² = 4, (-1)² = 1, (0)² = 0, (1)² = 1, (2)² = 4.
Step 8: Add the squared differences together: 4 + 1 + 0 + 1 + 4 = 10.
Step 9: Divide the total of the squared differences by the count of numbers: 10 / 5 = 2.
Step 10: The variance of the data set is 2.

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.