For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

₹0.0

Question: For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

Options:

Correct Answer: 8

Exam Year: 2020

Solution:

Mean = (10 + 12 + 14 + 16 + 18) / 5 = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.

For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

Step 1: Add all the numbers in the data set: 10 + 12 + 14 + 16 + 18.
Step 2: Calculate the total: 10 + 12 + 14 + 16 + 18 = 70.
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: 70 / 5 = 14.
Step 5: Subtract the mean from each number in the data set: (10-14), (12-14), (14-14), (16-14), (18-14).
Step 6: Calculate the results of the subtractions: -4, -2, 0, 2, 4.
Step 7: Square each of the results: (-4)² = 16, (-2)² = 4, (0)² = 0, (2)² = 4, (4)² = 16.
Step 8: Add all the squared results together: 16 + 4 + 0 + 4 + 16 = 40.
Step 9: Divide the total of the squared results by the count of numbers: 40 / 5 = 8.
Step 10: The variance of the data set is 8.

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.