Practice Aggregation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Aggregation is the process of combining many individual data values into a single summary statistic such as a sum, mean, count, or proportion.
Going from individual values to totals, averages, or other summaries.
Showing a random 20 of 50 problems.
Example 1
hardA statistic is robust if it is not strongly affected by outliers. Which aggregate is more robust: mean or median? Justify briefly.
Example 2
mediumA bookstore tracks -week sales: books. Find the weekly mean and the proportion of weeks above the mean.
Example 3
challengeA city's overall average commute time fell from to minutes, yet commute time rose in every neighborhood. Explain the mechanism and what data shift makes this consistent.
Example 4
mediumA company reports average employee salary rose from \$50k to \$55k year over year, yet every employee took a pay cut. How is this possible through aggregation?
Example 5
mediumA factory aggregates output across two shifts: day made units in hours, night made units in hours. Compute the combined units-per-hour rate.
Example 6
mediumA factory's three lines produce units (line 1), units (line 2), units (line 3) in a day. Defect rates are , , respectively. Aggregate defect rate?
Example 7
challengeConstruct a minimal Simpson's paradox: two groups where group 1 beats group 2 in EACH of two subcategories, yet group 2 wins overall. Give explicit small fractions.
Example 8
mediumA store sold items at $5, items at $8, and items at $20. What is the average selling price per item?
Example 9
mediumDaily temperatures for a week are aggregated to a single mean of . A meteorologist warns this is insufficient. What two aggregates together would describe the week better?
Example 10
easyMonthly sales (\$thousands): Jan–Mar: 50, 60, 55; Apr–Jun: 80, 90, 85; Jul–Sep: 40, 35, 45. Calculate quarterly totals and annual total. What pattern does aggregation reveal?
Example 11
easyName three common aggregation summary statistics.
Example 12
easyA dashboard shows total website visits per month. This single number is an example of what?
Example 13
mediumA scoreboard shows total points but not games played. What aggregation question can you not answer from it?
Example 14
mediumSimpson's Paradox: Hospital A has a 90% recovery rate overall. Hospital B has 85%. However, for severe cases: A has 70%, B has 75%; for mild cases: A has 98%, B has 95%. Explain the paradox.
Example 15
mediumSales by region: North (3 reps), South (1 rep). The CEO compares 'average sales per region' vs 'average sales per rep.' Compute both.
Example 16
easyTwo groups: group A has items summing to ; group B has items summing to . What is the combined (pooled) mean of all items?
Example 17
easyIs the average of two group averages always equal to the overall average? Yes or no.
Example 18
easyWhy is reporting only a mean test score per class potentially misleading?
Example 19
easyIn a survey, out of people answered 'yes'. What proportion is this?
Example 20
challengeConstruct a Simpson's paradox dataset: two groups, two subcategories, where in each subcategory Group 1's rate beats Group 2's, but Group 2 has a higher overall rate. Use small integer counts.