The question chooses the chart
Before drawing a chart, decide what the reader needs to find out. Most questions about data are one of four kinds: which group is biggest, what share of a whole each part takes, how something changed over time, or how a set of measurements is spread out.
Each kind of chart is built for one of these readings. A bar chart compares lengths, a pie chart compares angles as shares of a full turn, a line graph shows a value rising and falling over time, and a histogram shows how measurements are spread along a scale. The type of data matters too: categories, counts and measurements each suit different charts.
Comparing groups: a bar chart
Which club at a school is biggest? The art club has 12 members, the chess club 8 and the band 15. The clubs are categories, and the question compares their sizes.
A bar chart puts the categories side by side, each with a bar as tall as its count, all rising from 0. The eye compares the heights at once: the band is the biggest club, with 15 − 8 = 7 more members than the chess club.
The band’s bar reaches 15, art’s 12 and chess’s 8: the band is the biggest club.
Parts of a whole: a pie chart
What share of a day does a student spend asleep? The student sleeps for 9 hours, spends 7 hours at school and has 8 hours of free time: 9 + 7 + 8 = 24 hours, one whole day.
A pie chart shows each part as a share of the whole circle. Sleep is of the day, so its sector is . School is , and free time is . The angles add up to 360°. A bar chart of the same numbers would show that sleep takes the most hours, but not that the three parts make up one whole day.
The day as a whole circle: sleep 135°, school 105° and free time 120°, which add up to 360°.
Change over time: a line graph
How did the midday temperature change during one week? It was 24°C on Monday, 27°C on Tuesday, 25°C on Wednesday, 29°C on Thursday and 31°C on Friday.
A line graph puts time along the horizontal axis, in order, and plots one point for each reading. The points are joined by straight lines, so each segment shows a rise or a fall from one day to the next: up 3°C on Tuesday, down 2°C on Wednesday, up 4°C on Thursday and up 2°C on Friday. Over the week the temperature rose by 31 − 24 = 7°C.
The points may be joined because time runs on between one reading and the next. The tops of the club bars must not be joined by a line, because nothing lies between art and chess.
One point for each day, joined in order: the temperature dips on Wednesday and ends the week at 31°C, 7°C above Monday.
How measurements spread: a histogram
How are the heights of 27 students spread? Heights are measurements, so they are grouped into classes first: 3 students are from 130 to 140 cm tall, 8 from 140 to 150 cm, 11 from 150 to 160 cm and 5 from 160 to 170 cm. Check: 3 + 8 + 11 + 5 = 27.
A histogram draws one bar over each class, with the bars touching because the classes meet. It shows where the values are most crowded, here from 150 to 160 cm, and how they thin out on either side.
For a small set of values, a stem-and-leaf diagram shows the same shape and keeps every value: each height is written in its row, so none of the detail is lost. A histogram suits a larger set, where writing every value out would be too much.
The touching bars show the 27 heights. The tallest bar is over 150–160 cm, and the bars are lower toward either end.
The type of data narrows the choice
Name the type of data first. Categorical data, such as a favorite sport, are drawn as a bar chart, or as a pie chart when the categories share out one whole. Discrete data, counts such as the number of pull-ups a student can do, are drawn as a vertical line chart or a dot diagram, with nothing between the whole numbers. Continuous data, measurements such as times and heights, are grouped into classes and drawn as a histogram.
A chart that does not match its data or its question gives the wrong message. A pie chart cannot show answers where one person may give two, because its sectors would add up to more than the whole. A line joining categories claims values between them that do not exist. And favorite sports cannot be drawn as a histogram, because a histogram needs a number scale along its horizontal axis.
Worked example: Three Sets of Fitness Data and the Display That Suits Each
Question A PE teacher has three sets of data about one class: each student's favorite sport, the number of pull-ups each student can do, and each student's time for a 2.4 km run. (a) Choose a suitable display for each set of data, and give the reason from the type of data. (b) The run times, in minutes, of 12 students are 11.5, 12.0, 13.2, 13.9, 14.0, 14.6, 12.8, 15.1, 16.4, 13.5, 14.0 and 17.2. They are grouped into the classes 10 ≤ x < 12, 12 ≤ x < 14, 14 ≤ x < 16 and 16 ≤ x < 18 for a histogram. How many students are in the class 12 ≤ x < 14, and in which class does a time of 14.0 minutes belong?
1.A favorite sport is a name, so the data are categorical. A bar chart suits them: there is one bar for each sport, and the gaps between the bars show that the categories are separate. A pie chart would also do.
A favorite sport is a name, so the data are categorical, and a bar chart has one separate bar for each sport. 2.A number of pull-ups is a count, 0, 1, 2 and so on, so the data are discrete. A dot diagram or a vertical line chart suits them, because each whole number has its own column of dots or its own line, and nothing is drawn between the whole numbers.
A number of pull-ups is a count, so the data are discrete, and a dot diagram has a column of dots at each whole number. 3.(a) A run time is a measurement and can be any value, such as 13.27 minutes, so the data are continuous. A histogram suits them: the times are grouped into classes, and the bars touch because each class starts where the class before it ends.
(a) A run time is a measurement, so the data are continuous, and a histogram groups the times into classes whose bars touch. 4.Tally each time into its class. The class 12 ≤ x < 14 includes 12.0 but does not include 14.0, so a time of 14.0 goes into 14 ≤ x < 16. The tallies are 1, 5, 4 and 2. Check: 1 + 5 + 4 + 2 = 12 students.
Tally each time into its class. 14.0 is left out of 12 ≤ x < 14 and goes into 14 ≤ x < 16. The tallies are 1, 5, 4 and 2. 5.(b) 5 students are in the class 12 ≤ x < 14: their times are 12.0, 13.2, 13.9, 12.8 and 13.5. Each time of 14.0 minutes belongs to the class 14 ≤ x < 16.
(b) 5 students are in the class 12 ≤ x < 14, and 14.0 belongs to 14 ≤ x < 16.
Answer: (a) a bar chart for the sports, which are categorical; a dot diagram or a vertical line chart for the pull-ups, which are discrete; a histogram for the run times, which are continuous; (b) 5 students, and 14.0 belongs to 14 ≤ x < 16
Common mistakes
- Drawing a histogram for the favorite sports. A histogram needs a number scale along its horizontal axis, and the sports have no order and no scale. Separate bars in a bar chart are correct for categories.
- Counting a time of 14.0 minutes in both classes, or in 12 ≤ x < 14. The sign < at the upper end means that 14 is left out of that class, and ≤ at the lower end of the next class means that it is included there. Every value belongs to exactly one class.