One-Variable Data: Distributions and Measures of Center and Spread
Mean, median, mode, and range show up on nearly every test — and the questions are usually quick points if you know the rules. The trick is reasoning about how outliers and spread shift these numbers.
Data 2, 4, 9: mean = 5, median = 4 (the middle value).
Adding the outlier 28 pulls the mean up, but the median stays at 5.
Reading frequency tables: sometimes data is given as a table of values and how many times each occurs. To find the median, imagine the full sorted list (don't just take the middle row). To find the mean, multiply each value by its frequency, add those up, and divide by the total frequency.
Check your understanding with a question from this topic:
The mean of 8 numbers is 12.5. If one number (16) is removed, what is the mean of the remaining 7 numbers?
Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).
Worked examples
The ages of 6 players on a team are 14, 15, 15, 16, 18, 20. What is the median age?
The mean of 5 numbers is 18. A sixth number is added and the new mean of all 6 numbers is 20. What is the value of the sixth number?
Two data sets each have 5 values. Set A: 10, 10, 10, 10, 10. Set B: 2, 6, 10, 14, 18. Both have the same mean of 10. Which statement correctly compares their standard deviations?
Common pitfalls
The median is the middle of the sorted list. If you take the middle of an unsorted list, you'll get the wrong answer. Always reorder the values first.
An extreme value drags the mean toward it but leaves the median mostly unchanged. Questions love to test which measure 'better represents' skewed data — the answer is usually the median.
In a frequency table, each value can occur many times. To find the median you must account for every occurrence, not just pick the value in the middle row of the table.
The test never asks you to compute it — only to compare. Don't waste time with the formula; just judge which data set is more spread out from its mean.
Key takeaways
Mean = total ÷ count; rearrange to total = mean × count to handle added/removed values.
Median is the middle of the sorted list (average the two middle values if the count is even).
Mode is the most frequent value; range is max minus min.
Outliers pull the mean but barely move the median — median is resistant.
Compare standard deviation by spread: more scattered data = larger standard deviation; identical values = 0.
Watch & learn
Curated Khan Academy walkthroughs on One-Variable Data: Distributions and Measures of Center and Spread. They're complementary to this lesson — watch one if a written explanation isn't clicking, or after to reinforce.
Try it yourself
5 practice questions on One-Variable Data: Distributions and Measures of Center and Spread, drawn from the question bank. The tutor is one click away if you get stuck.