A weighted mean counts each displayed value as many times as its frequency says. When two data sets contain the same number of values, comparing their totals is enough; a Desmos table can keep each value paired with its frequencies. Averaging only the displayed values can falsely suggest equal means because it ignores how often each value occurs.
Hints
- Hint 1
The mean is the total divided by the number of values. Both sets have the same count, so which one calculation could you compare instead of finding both means?
- Hint 2
A frequency tells you how many times a value occurs. For example, contributes to A's total. How can you use every row to build the two totals?
Step-by-step
Compare weighted totals
Step 1Use the equal counts
Each set has values, and the mean is the total divided by the count. So and , where and are their totals. With the same denominator, the larger total gives the larger mean. The denominator is , not the five table rows.
- Step 2
Turn frequencies into totals
A frequency counts repeated values: A has two s, so that row contributes . Multiply each value by its frequency in the matching column:
- Step 3
Find A's total in Desmos
Enter the values as , A's frequencies as , and B's as , keeping each row together. Type . Desmos multiplies the paired entries and adds them, showing .
- Step 4
Find B's total
Add to use B's frequency column. Desmos shows .
- Step 5
Compare the means
Since and both totals are divided by , A has the greater mean. The mean of data set A is greater than the mean of data set B. Choice D.