Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Numerical data are easier to understand when you can see them, and sixth grade adds three number-line displays. A dot plot puts one dot above the number line for each value, which works well for small data sets and shows every individual value. A histogram groups values into equal-width intervals, like 0 to 9 and 10 to 19, and draws a bar for how many values fall in each interval, which suits larger data sets. A box plot summarizes data with five numbers: minimum, lower quartile, median, upper quartile and maximum.
Each display reveals some features and hides others. Dot plots show clusters and gaps clearly. Histograms show overall shape but lose the exact values. Box plots make it easy to compare the middle half of two groups but hide details such as how many values there are. Students should be able to make each display accurately, including choosing a sensible scale and equal intervals, and to read each one. Building a box plot also requires finding quartiles, which is the median of the lower half and the median of the upper half of the ordered data.
Using intervals like 0 to 5 and 6 to 20 distorts the shape. Every bar must cover the same width.
A longer section of a box plot does not hold more data. Each section contains about a quarter of the values; a longer one means those values are more spread out.
Histograms of numerical data have touching bars because the intervals are continuous. Gaps belong to bar graphs of categories.
Find the five-number summary for the data 3, 5, 6, 8, 9, 10, 12, 15, 18 and describe the box plot.
Answer: Five-number summary: 3, 5.5, 9, 13.5, 18.
Use one data set from the class, such as arm spans, and display it all three ways side by side. Discussing what each display shows best helps students choose displays sensibly.
Assessment items include completing a display from data, reading the median or quartiles off a box plot, and finding how many values fall in a histogram interval.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 5
There are 7 values in order, so the median is the 4th value: 5.
Answer: A) Dot plot
A dot plot places a dot for every value. Histograms and box plots summarize the data.
Answer: 3.5
The lower half is 1, 3, 4, 6. Its median is (3 + 4) ÷ 2 = 3.5.
Answer: C) 13
Add the frequencies: 4 + 7 + 2 = 13 values.
Answer: D) About one half
The box covers the middle half of the data, from the lower quartile to the upper quartile.
A full lesson with slides, activities and an exit ticket on dot plots, histograms and box plots, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.SP.B.4 with an answer key, ready in about a minute.
Make a worksheet →Turn dot plots, histograms and box plots into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Dot plots, histograms and box plots, all drawn on a number line.
The minimum, lower quartile, median, upper quartile and maximum of a data set. These five values are used to draw a box plot.