math class 678 4-in-1 skill sheets
6.SP.B.4 6th Grade Statistics & Probability

Data Displays: Dot/Histogram/Box Plots

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

How to explain it

At this standard, students read and interpret three types of numerical data displays: a dot plot, which stacks one dot for each value; a histogram, which groups values into equal intervals shown as touching bars whose height is the count; and a box plot, which marks the five-number summary (minimum, first quartile, median, third quartile, maximum). Students read counts, intervals, and summary values directly from each display.

The anchor students hold onto: Match the display to the data: a dot plot for exact values, a histogram for grouped intervals, a box plot for the five-number summary.

Reading these displays prepares students to summarize numerical data with measures of center and variability, including the interquartile range and mean absolute deviation (6.SP.B.5).

Worked examples

Example 1 Histogram
Counts: 4 in 0–9, 8 in 10–19.
Step 1Equal intervals of width 10
Step 2Bar height = count for that interval
Step 3Tallest bar: 10–19 (8 people)
Step 4Bars touch; no gaps between them
AnswerPeak interval: 10–19
Example 2 Box Plot
Summary: 4, 7, 10, 14, 20.
Step 1Whiskers: min 4 to max 20
Step 2Box: Q1 7 to Q3 14
Step 3Line inside box at median 10
Step 4Box holds the middle 50% of data
AnswerMedian 10; box 7 to 14

Common mistakes

What students write Counting the number of bars in a histogram to find total data values
The fix Each bar shows how many values are in that interval — add ALL bar heights to count total values.
Try this Use the box plot of race times (seconds). A student says the faster runners (min to median) are more spread out than the slower runners (median to max). Is the student correct? Explain using the plot values.
What students write Thinking a longer section of a box plot means more data points are there
The fix Every section holds the same 25% of the data; a longer section means more SPREAD, not more points.
Try this A student says this histogram shows 3 values in all — one per bar. Student's Work: "I count 3 bars, so there are 3 values." Find the error and give the correct total count.

Teacher tip

Head off the two predictable errors before they happen. First: Each bar shows how many values are in that interval — add ALL bar heights to count total values. Second: Every section holds the same 25% of the data; a longer section means more SPREAD, not more points.