For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)

For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)

Step 1: Identify the data set. The data set is 3, 3, 3, 3, 3.
Step 2: Understand what variance means. Variance measures how much the numbers in a data set differ from the average (mean).
Step 3: Calculate the mean (average) of the data set. Add all the numbers together: 3 + 3 + 3 + 3 + 3 = 15. Then divide by the number of values: 15 / 5 = 3.
Step 4: Find the difference between each number and the mean. Since all numbers are 3, the difference is 3 - 3 = 0 for each number.
Step 5: Square each difference. 0 squared is 0.
Step 6: Calculate the average of these squared differences. Since all squared differences are 0, the average is 0.
Step 7: Conclude that the variance is 0 because there is no difference among the numbers.

Variance – Variance measures the spread of a set of numbers; it is the average of the squared differences from the mean.
Constant Data Set – When all values in a data set are the same, the variance is zero because there is no spread.