The Mean from Frequency Counts

A frequency table tells you how many times each value showed up, not the list of 200 numbers itself. Adding 0 fourteen times, then 1 eight times, then 2 ten times, would eventually get you the right answer — but multiplication does the repeated addition for you. Each value times its frequency gives the total contribution of that value to the sum, and adding those products across every row gives the grand total. Divide that total by the number of data points (the sum of all the frequencies, not the number of rows) and you have the mean.

The reason this matters on this part of the test is that frequency tables are a compressed way to hand you a full data set. The mean is still defined the same way it always is — total divided by count — the table just organizes the counting for you. Once you see a value column and a frequency column sitting side by side, your job is always the same: multiply down each row, add the products, divide by total frequency.

This sits right next to weighted averages and two-way tables because the underlying move is identical: nothing in statistics is ever just a plain average of the labels you see. Values that appear more often pull the mean toward themselves, exactly the way a weighted average lets some scores count more than others. Get comfortable here and weighted-average problems with percentages or credit hours stop looking like a different topic.