Solved: Square Footage of Housing The frequency

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Consider Square Footage of Housing The frequency distribution below represents the square footage of a random sample of 500 houses that are owner occupied year round and the data is given below.

\(\begin{array}{|l|l|l|l|l|} \hline \text { Square Footage } & {f_{i}} & \begin{array}{l} \text { Mid values } \\ x_{i} \end{array} & x_{i} f_{i} & x_{i}^{2} f_{i} \\ \hline 0-499 & 5 & 250 & 1250 & 312500 \\ \hline 500-999 & 17 & 750 & 12750 & 9562500 \\ \hline 1000-1499 & 36 & 1250 & 45000 & 56250000 \\ \hline 1500-1999 & 121 & 1750 & 211750 & 370562500 \\ \hline 2000-2499 & 119 & 2250 & 267750 & 602437500 \\ \hline 2500-2999 & 81 & 2750 & 222750 & 612562500 \\ \hline 3000-3499 & 47 & 3250 & 152750 & 496437500 \\ \hline 3500-3999 & 45 & 3750 & 168750 & 632812500 \\ \hline 4000-4499 & 22 & 4250 & 93500 & 397375000 \\ \hline 4500-4999 & 7 & 4750 & 33250 & 157937500 \\ \hline \text { Total } & \Sigma f_{i}=500 & \Sigma x_{i}=25000 & \Sigma x_{i} f_{i}=1209500 & \Sigma x_{i}^{2} f_{i}=3336250000 \\ \hline \end{array}\)

In the table, column 1 contains the class, column 2 contains the frequency of each class and column 3 contains the midpoint of each class. Column 4 contains the product of midpoint and frequency is \(x_{i} f_{i}\) where midpoint is \(x_{i}\) and frequency is \(f_{i^{\prime}}\) for each class. Column 5 contains the product of squared midpoint and frequency is \(x_{i} f_{i}\).