If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

₹0.0

Question: If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

Options:

Correct Answer: 6

Exam Year: 2022

Solution:

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

If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

Step 1: Add all the numbers in the data set: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9.
Step 2: Count how many numbers are in the data set. There are 8 numbers.
Step 3: Divide the total from Step 1 by the count from Step 2 to find the mean: (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5.
Step 4: Subtract the mean from each number in the data set and square the result: (2-5)², (4-5)², (4-5)², (4-5)², (5-5)², (5-5)², (7-5)², (9-5)².
Step 5: Calculate each squared difference: (2-5)² = 9, (4-5)² = 1, (4-5)² = 1, (4-5)² = 1, (5-5)² = 0, (5-5)² = 0, (7-5)² = 4, (9-5)² = 16.
Step 6: Add all the squared differences together: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16.
Step 7: Divide the total from Step 6 by the count from Step 2 (8) to find the variance: (9 + 1 + 1 + 1 + 0 + 0 + 4 + 16) / 8 = 4.

Mean – The average of a data set, calculated by summing all values and dividing by the number of values.
Variance – A measure of how much the values in a data set differ from the mean, calculated as the average of the squared differences from the mean.