Where this sits. This is one of the four shape, data, and chance families — the middle ground, where the formula sheet does most of the remembering and your job is choosing the right formula. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsThirteen drills for this family, one skill each, ten problems at a timeGo to the drills ↓Reading tables, bar graphs, line graphs, dot plots, and histograms without being fooled by them, and the four summary numbers — mean, median, mode, and range — that each describe a pile of data in one figure.
The test also asks for a weighted mean now and then, and asks which summary number is the honest one to use. That last question is the interesting one, and it is not really a mathematics question: it is a question about what the data is for.
What the test asks in this family
- The meanQuiz 28
- The medianQuiz 28
- The modeQuiz 28
- The rangeQuiz 28
- Reading a tableQuiz 28 · Quiz 38
- Choosing which summary number is the honest oneQuiz 28
- A weighted meanQuiz 38
- Bar graphs, line graphs, dot plots, and histogramsQuiz 38
- Scatter plotsQuiz 38
All 9 have something on this site.
Six questions across this family. Type an answer and press Check. You get the reasoning for every one, right or wrong.
- Find the mean of 7, 12, 9, 4. 8. The mean is the fair share: add them up and divide by how many there are. 7 + 12 + 9 + 4 = 32, and 32 ÷ 4 = 8. It is the number every value would be if the total were shared out evenly.
- Find the median of 3, 9, 4, 12, 7. 7. The median is the middle value — but only after you sort them: 3, 4, 7, 9, 12. Now the middle is 7. Reading the middle of the unsorted list gives 4, which is the mistake this question is built to catch. With an even count there is no single middle, so you take the mean of the two.
- Find the mode of 5, 2, 5, 8, 2, 5. 5. The mode is the one that turns up most often. 5 appears three times, 2 appears twice, 8 once. It is the only one of the four summary numbers that has to be a value actually in the list.
- Find the range of 14, 6, 21, 9. 15. The range is the spread: the largest minus the smallest, so 21 − 6 = 15. It says nothing about where the values sit in between — only how far apart the two ends are.
- Four people at a small firm earn $30,000, $32,000, $31,000 and $300,000. Which describes what most of them earn better, the mean or the median? The median. The mean here is $98,250, which describes nobody in the room — one very large value has dragged it up. The median is $31,500, which is close to what three of the four actually earn. The test asks this kind of question, and so does the world: when one value is far out of line with the rest, the mean stops being honest.
- On a bar graph, Tuesday's bar reaches 45 and Thursday's reaches 28. How many more on Tuesday? 17. Read each bar against the scale first, then do the arithmetic: 45 − 28 = 17. Most graph questions on the test are like this — the reading is the work and the sum is straightforward. Check what the scale counts in before you read a value; bars often go up in fives or tens, not ones.
Missed one? Quiz 28 in Learn it below covers all four summary numbers, and Quiz 38 covers the graphs — bar, line, histogram, dot plot and scatter — along with the weighted mean. Every part of this family now has a lesson.
Want more than these six questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 28Mean, Median, Mode, and RangeThe four summary numbers, what each one hides, and when to use which.
- Quiz 38What the Graph SaysBar graphs, line graphs, histograms, dot plots and scatter plots — how to read them, how they mislead, and the weighted mean.
Two quizzes, and with them this family is complete: every topic listed above now has a lesson.
Thirteen short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 8.01The mean · calculator allowed
- 8.02The median
- 8.03The mode and the range
- 8.04The missing value that gives a stated mean · calculator allowed
- 8.05A weighted mean · calculator allowed
- 8.06Read a table
- 8.07Read a bar graph
- 8.08Read a line graph
- 8.09Read a circle graph · calculator allowed
- 8.10Read a dot plot and a histogram
- 8.11Read a box plot
- 8.12Scatter plots: the trend and the correlation
- 8.13Which measure fits best, and what an outlier does
No app for this family yet.
No worksheet for this family yet.
- Khan Academy, math · free videos and practice. Search it for mean median mode, reading bar graphs, histograms. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up data analysis and statistics in the contents of either.
On to probability and counting — a small family, and the one most often left out of a study plan. It is worth an afternoon because it is small: a few questions on the test, and not much to learn.