Question

What is the sample variance of the following numbers
A) 4.5
B) 5.5
C) 3.5
D) 2.5

Answer 1

The sample variance of the given numbers is 1.67.

Step-by-step explanation:

The sample variance of a set of numbers measures the variability or spread of the numbers around their mean. To calculate the sample variance, you need to follow these steps:

1. Calculate the mean of the numbers.
2. Subtract the mean from each number and square the result.
3. Calculate the sum of the squared differences.
4. Divide the sum by the number of data points minus one to get the sample variance.

For the given numbers:

• A) 4.5
• B) 5.5
• C) 3.5
• D) 2.5

Let's calculate the sample variance:

• Mean = (4.5 + 5.5 + 3.5 + 2.5) / 4 = 4.0
• Squared differences: (4.5 - 4.0)^2, (5.5 - 4.0)^2, (3.5 - 4.0)^2, (2.5 - 4.0)^2
• Sum of squared differences: (0.5)^2 + (1.5)^2 + (-0.5)^2 + (-1.5)^2 = 0.25 + 2.25 + 0.25 + 2.25 = 5.0
• Sample variance: 5.0 / (4 - 1) = 5.0 / 3 = 1.67

Therefore, the sample variance of the given numbers is 1.67.