The book cost (in dollars) for one semester's books are given below for a sample of five college students. Calculate the sample variance of the book costs.275, 100, 380, 480, 260
A) 380.00
B) 142.32
C) 20,255.00
D) 299.00

Question

Quizplus · Accepted Answer

DC) The sample variance is calculated using the formula: $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$, where $x_i$ are the sample values, $\bar{x}$ is the sample mean, and $n$ is the sample size. First, calculate the mean: $\bar{x} = \frac{275 + 100 + 380 + 480 + 260}{5} = 299$. Then, calculate the sum of squared deviations: $\sum (x_i - \bar{x})^2 = (275-299)^2 + (100-299)^2 + (380-299)^2 + (480-299)^2 + (260-299)^2 = 20250$. Finally, divide by $n-1 = 4$: $s^2 = \frac{20250}{4} = 5062.5$. It seems there was a mistake in my calculation as none of the options match this result. Let's correct the process:To find the correct sample variance, we follow the steps but ensure accurate calculation:1. Calculate the mean: $\bar{x} = \frac{275 + 100 + 380 + 480 + 260}{5} = 1495 / 5 = 299$.2. Calculate each squared deviation from the mean, sum them, and divide by $n-1$: $(275-299)^2 + (100-299)^2 + (380-299)^2 + (480-299)^2 + (260-299)^2 = (-24)^2 + (-199)^2 + 81^2 + 181^2 + (-39)^2 = 576 + 39601 + 6561 + 32761 + 1521 = 81020$.3. Divide by $n-1 = 4$: $s^2 = \frac{81020}{4} = 20255$.D) The correct calculation of the sample variance should indeed result in a specific value based on the formula and steps provided. However, the initial explanation mistakenly led to an incorrect conclusion. The correct sample variance calculation involves summing the squared differences between each observation and the mean, then dividing by the number of observations minus one. The error in the explanation was in the final computation and matching with the provided options.

The Book Cost (In Dollars) for One Semester's Books Are