Math 1 · Unit 12 · Lesson 1 · part 2 of 5

Three pictures, and the three questions

Unit 10 looked at two quantities at once, as scatter plots.

Three pictures, and the three questions

Unit 10 looked at two quantities at once, as scatter plots. This unit looks at one quantity at a time: a list of test scores, heights, or song downloads. The list is a data set, and the way its values are spread along the number line is its distribution. Whenever you meet a data set, ask the same three questions, in the same order, the way you ask the three family questions about a function. What shape is it? Where is the center? How spread out is it? Then say the answer in a sentence about the context.

Start with the three pictures from middle school and what each is good for.

Dot plotOne dot for every value, stacked up when values repeat. You see every value, which is great for a small data set and crowded for a big one.

HistogramGroups the values into bins, intervals of the same width, and draws a bar for how many fall in each. Individual values disappear, but the shape is easy to see. Changing the bin width changes the picture.

Box plotBuilt from the 5-number summary: the minimum, the first quartile Q1, the median, the third quartile Q3, and the maximum. The box holds the middle half of the data and the whiskers reach out to the ends. It shows the spread in four quarters, but not every value.

Mrs. Jones asked the 25 students in her class how many songs they downloaded last week: 10, 20, 12, 14, 12, 27, 88, 2, 7, 30, 16, 16, 32, 25, 15, 4, 0, 15, 6, 1, 0, 15, 12, 10, 7. Here is the same data three ways. Technology does the drawing so your time goes to reading the picture. Slide the bin width and watch the histogram change.

The 5-number summary is 0, 6.5, 12, 18, 88. The box runs from 6.5 to 18 with the median line at 12, and one whisker stretches all the way out to 88: one student downloaded far more than everyone else. (Lesson 4 shows why the tool draws that 88 as a separate dot.)

Which picture for which question? To see every value or find one student: the dot plot. To see the shape of a big data set: the histogram. To compare the middle half and the spread of two groups: the box plot. For the class period data from 11 schools, a dot plot is fine. For hundreds of students, a histogram or a box plot.

Where to go next

Next: Shape: find the tailThe first of the three questions is shape . All the partsPictures of Data and Their Shapes