Which of the following data sets has the highest variance? A: {1, 2, 3}, B: {1,

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Question: Which of the following data sets has the highest variance? A: {1, 2, 3}, B: {1, 1, 1}, C: {1, 5, 9}, D: {2, 2, 2}. (2020)

Options:

Correct Answer: C

Exam Year: 2020

Solution:

Variance of A = 0.67, B = 0, C = 12, D = 0. Thus, C has the highest variance.

Which of the following data sets has the highest variance? A: {1, 2, 3}, B: {1, 1, 1}, C: {1, 5, 9}, D: {2, 2, 2}. (2020)

Which of the following data sets has the highest variance? A: {1, 2, 3}, B: {1, 1, 1}, C: {1, 5, 9}, D: {2, 2, 2}. (2020)

Step 1: Understand what variance means. Variance measures how spread out the numbers in a data set are from the average (mean).
Step 2: Calculate the mean (average) for each data set.
Step 3: For data set A: {1, 2, 3}, the mean is (1 + 2 + 3) / 3 = 2.
Step 4: For data set B: {1, 1, 1}, the mean is (1 + 1 + 1) / 3 = 1.
Step 5: For data set C: {1, 5, 9}, the mean is (1 + 5 + 9) / 3 = 5.
Step 6: For data set D: {2, 2, 2}, the mean is (2 + 2 + 2) / 3 = 2.
Step 7: Calculate the variance for each data set using the formula: variance = average of the squared differences from the mean.
Step 8: For data set A: Variance = [(1-2)² + (2-2)² + (3-2)²] / 3 = (1 + 0 + 1) / 3 = 0.67.
Step 9: For data set B: Variance = [(1-1)² + (1-1)² + (1-1)²] / 3 = (0 + 0 + 0) / 3 = 0.
Step 10: For data set C: Variance = [(1-5)² + (5-5)² + (9-5)²] / 3 = (16 + 0 + 16) / 3 = 12.
Step 11: For data set D: Variance = [(2-2)² + (2-2)² + (2-2)²] / 3 = (0 + 0 + 0) / 3 = 0.
Step 12: Compare the variances: A = 0.67, B = 0, C = 12, D = 0.
Step 13: Identify the highest variance, which is from data set C.

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