Question

matteo is calculating the variance of his expenses for the week using a spreadsheet. he has calculated the mean using the formula \=average(b2:b13)\, and then found the squared differences of each data point and the mean. then he added up the squared differences using the formula \=sum(d2:d13)\. what is the last step for him to find the variance? he needs to subtract the mean from the sum using the formula \d11 - b10\. he needs to divide the sum by 7 using the formula \=d11/7\. he needs to multiply the sum by 7 using the formula \=d11*b7\.

Explanation:

Step1: Recall variance formula

The variance of a sample is given by $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, where $x_{i}$ are the data - points, $\bar{x}$ is the mean, and $n$ is the number of data - points. In a spreadsheet context, after finding the sum of the squared differences $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$ (let's assume this sum is in cell D11) and knowing the number of data - points $n = 7$, we need to divide the sum by $n-1$. But if we assume we are calculating the population variance (divided by $n$), we divide the sum by the number of data points. Here, we divide the sum (in D11) by 7.

Step2: Identify the operation

The operation to find the variance is to divide the sum of the squared differences (stored in cell D11) by the number of data points (7). In spreadsheet terms, the formula is "=D11/7".

Answer:

He needs to divide the sum by 7 using the formula "=D11/7".