Calculate the variance of the data set {4, 8, 6, 5, 3}.

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Question: Calculate the variance of the data set {4, 8, 6, 5, 3}.

Options:

Correct Answer: 2.5

Solution:

Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.

Calculate the variance of the data set {4, 8, 6, 5, 3}.

Calculate the variance of the data set {4, 8, 6, 5, 3}.

Step 1: Add all the numbers in the data set: 4 + 8 + 6 + 5 + 3.
Step 2: Calculate the total: 4 + 8 = 12, 12 + 6 = 18, 18 + 5 = 23, 23 + 3 = 26.
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: 26 / 5 = 5.2.
Step 5: Subtract the mean from each number in the data set: (4 - 5.2), (8 - 5.2), (6 - 5.2), (5 - 5.2), (3 - 5.2).
Step 6: Calculate each result: -1.2, 2.8, 0.8, -0.2, -2.2.
Step 7: Square each of the results: (-1.2)² = 1.44, (2.8)² = 7.84, (0.8)² = 0.64, (-0.2)² = 0.04, (-2.2)² = 4.84.
Step 8: Add all the squared results together: 1.44 + 7.84 + 0.64 + 0.04 + 4.84.
Step 9: Calculate the total of the squared results: 1.44 + 7.84 = 9.28, 9.28 + 0.64 = 9.92, 9.92 + 0.04 = 9.96, 9.96 + 4.84 = 14.8.
Step 10: Divide the total of the squared results by the count of numbers (5): 14.8 / 5 = 2.96.
Step 11: The variance of the data set is 2.96.

Mean Calculation – The mean is the average of a data set, calculated by summing all values and dividing by the number of values.
Variance Calculation – Variance measures the spread of a data set by averaging the squared differences from the mean.
Data Set – Understanding the data set is crucial for accurate calculations of mean and variance.