Central angle from a percentage
\(\text{angle}=\frac{\text{percent}}{100}\times 360^\circ\)
angle = 25 / 100 × 360° = 90°
Tahat Just Math · Self-paced practice
Read, Build and Summarize Data
Turn raw numbers into graphs and averages, one objective at a time.
- Construct and interpret circle graphs and central angles.
- Read line graphs and bar graphs.
- Build frequency distributions and histograms.
- Find the mean, median and mode, including from grouped data.
248 questions · 11 learning objectives
Objectives 1–3
Construct, calculate and interpret circle graphs
A circle graph shows how a whole is divided among categories. One full circle measures \(360^\circ\), so each category's central angle matches its share of the total.
Central angle from a count
\(\text{angle}=\frac{\text{category count}}{\text{total count}}\times 360^\circ\)
Objectives 4–5
Read line graphs and bar graphs
Use a line graph to follow change over time. Use a bar graph to compare categories. Read the axis labels and scale before comparing values.
Line graph
Find the value on the horizontal axis, move to the line, then read across to the vertical axis.
Bar graph
Read each bar's height from the scale. Then add, subtract or compare as the question asks.
Objectives 6–7
Build frequency distributions and histograms
- Choose equal-width intervals that cover the full range of the data.
- Place each value in exactly one interval and count its frequency \(f\).
- Check that the frequencies add to the number of data values.
- Draw one bar per interval. In a histogram, neighboring bars touch.
Objectives 8–11
Mean, median and mode
Mean
\(\bar{x}=\frac{\sum x}{n}\)
Add the values, then divide by how many values there are.
Median
Put the data in order. With an even number of values, average the two middle values.
Mode
The value that appears most often. A data set can have one mode, more than one, or none.
Mean of a frequency distribution
\(\bar{x}=\frac{\sum xf}{\sum f}\)
Multiply each interval midpoint \(x\) by its frequency \(f\). Add those products and divide by the total frequency.
Interactive playground
Build a circle graph from a percentage
Change the percentage to see how its share of the circle and central angle change.
37% of the circle is \(133.2^\circ\).
Central angle = percentage \(\times 3.6^\circ\)
Try \(25\%\), \(50\%\) and \(75\%\). The category and the remainder should always add to \(100\%\).
Line graph: change the values
Move a slider to change one day's value and watch the line bend.
Bar graph: change the heights
Each slider sets the height of one bar. Compare the categories and their total.
Frequency distribution and histogram
Change the frequency of each class interval. The histogram bars touch, and the grouped mean uses the class midpoints.
Mean = \(\frac{\sum xf}{\sum f}\)
Mean, median and mode
Edit the data set (numbers separated by commas). The chart shows each value in order, with the mean and median marked.
Learn by doing
Guided examples by skill
Open a skill, read the idea, then work through one example a step at a time. Use each question’s hint and step-by-step solution controls in Practice problems as needed.
Chapter 15 · Mock exam
A focused 20-question test
Questions are selected at random from the objectives you choose, with at least one question from each selected objective. Answer in any order, flag questions to revisit, and review everything before you submit. Your score and answer review appear at the end. Use your school-approved tablet; phones should remain put away under classroom rules.
- 20random questions
- 40 minutesauto-submits when time ends
- Tab & focus monitoringends after 3 departures
Switching tabs or focusing another window is counted. Some split-screen modes keep both pages focused and visible, which a website cannot detect. This is not secure proctoring.
The test requests fullscreen when you start. Exiting fullscreen is recorded and pauses the test until you return to fullscreen. If fullscreen is unavailable, you can choose to continue without it.
Focused practice
Choose a learning objective
Practice one skill at a time, or use the full assessment from the hero section to review the entire chapter.
Random practice
Mixed practice across every objective
Chapter 15 contains 248 questions across 11 learning objectives. Choose any number of questions you like. A random set takes one question from each objective first, so a set of 8 or more questions covers the whole chapter.