HSS.ID.A.1Common CoreMathStatistics and ProbabilityGrades 9-12
HSS.ID.A.1: Dot Plots, Histograms and Box Plots
In plain English: HSS.ID.A.1 is the Common Core statistics standard that asks students to represent a single numerical data set with plots on the real number line: dot plots, histograms and box plots. Students build each display from raw data, including the five-number summary for a box plot, and choose the plot that fits the data. It is usually taught in Algebra I or an introductory statistics unit.
Represent data with plots on the real number line (dot plots, histograms, and box plots).
Common Core State Standards for Mathematics · Domain: Interpreting Categorical and Quantitative Data (ID) · Cluster: Summarize, represent, and interpret data on a single count or measurement variable Also written as HSS-ID.A.1 or S-ID.1 · Official standard
Students learn to display one numerical variable on the real number line in three ways. A dot plot places one dot per value; a histogram groups values into equal-width bins and shows the count in each; a box plot shows the five-number summary (minimum, first quartile, median, third quartile, maximum) drawn to scale. Students build each display by hand from raw data before using technology, so they know what every mark means.
The lesson also asks students to choose a display. Dot plots suit small data sets, histograms suit larger data sets where shape matters, and box plots suit quick summaries and side-by-side comparisons. Describing and comparing distributions in depth is the focus of HSS.ID.A.2 and HSS.ID.A.3; here students read basic facts from each plot to check that it was built correctly.
Learning Objectives
By the end of this lesson, students will be able to:
Draw a dot plot of a numerical data set on an evenly scaled number line
Choose bins, make a frequency table and draw a histogram with touching bars
Find the five-number summary of a data set with an odd or even number of values and draw the box plot to scale
Read counts, the median, quartiles and ranges from each display
Choose the display that fits the size of the data set and the question being asked
Prior Knowledge Required
Students should already be comfortable with:
Displaying numerical data in dot plots, histograms and box plots at a basic level 6.SP.B.4
Finding the median and interquartile range of a data set 6.SP.B.5
Placing decimals and fractions on a number line with an even scale
Write this list on the board without comment: the number of books 12 students read over the summer.
Warm-Up Prompt
"0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 9. Sketch a picture of these numbers that would let a parent see in two seconds how many books a typical student read. What would your picture hide?"
Give students 3 minutes, then collect two or three sketches. Some students draw a bar graph with one bar per student, others draw tallies above a number line. Point out that the tally picture already is a dot plot, and that it makes the value 9 stand out. Tell students that today they learn three standard ways to put one numerical variable on a number line, and when each one is the right tool.
Direct Instruction20 minutes
Part 1: Dot plots. Draw a number line that covers the data with equal spacing, then place one dot per value, stacking repeated values. A dot plot keeps every value, so it works best for small data sets with few distinct values.
Part 2: Histograms. Choose a bin width, list back-to-back bins of that width that cover the data, count the values in each bin, and draw touching bars whose heights are the counts. In this lesson a value on a boundary goes in the bin that starts with it, so 20 belongs to 20-29. The vertical axis shows frequency, and the horizontal axis is a number line for the variable.
Part 3: Box plots. Order the data and find the five-number summary:
Order the values from least to greatest and count them (n).
Find the median: the middle value if n is odd, or the mean of the two middle values if n is even.
Split the list into a lower half and an upper half. When n is odd, leave the median out of both halves.
Find Q1 and Q3: the medians of the lower and upper halves.
Draw to scale above a number line: a box from Q1 to Q3, a line inside it at the median, and whiskers out to the minimum and maximum.
Tell students that this split-the-halves method is the one many graphing calculators use. Some software computes quartiles with a slightly different rule, so answers can differ by a small amount. Work through the examples below.
Dot plot
Number of siblings reported by 14 students: 2, 1, 0, 3, 2, 1, 2, 4, 1, 2, 0, 3, 1, 2.
Equation: Stacks: 2 dots at 0, 4 at 1, 5 at 2, 2 at 3, 1 at 4 (2 + 4 + 5 + 2 + 1 = 14)
Histogram
Commute times in minutes for 20 students: 5, 8, 9, 10, 12, 12, 15, 15, 18, 19, 20, 22, 24, 25, 25, 28, 30, 34, 38, 45. Use bins 0-9, 10-19, 20-29, 30-39, 40-49.
Equation: Bar heights 3, 7, 6, 3, 1 (total 20); see Diagram 2
Box plot, odd number of values
Minutes 11 students took to solve a logic puzzle: 4, 6, 7, 7, 9, 10, 12, 13, 15, 18, 22.
Show Diagram 1: the puzzle data as a dot plot directly above its box plot. Ask students to count the dots on each side of each box line (2 or 3 dots in every quarter) so they see that the box plot compresses the dot plot into five numbers. Then show Diagram 2 and ask what a parent can and cannot learn from it: they can see that most commutes are 10-29 minutes, but not the exact longest time.
Guided Practice15 minutes
Pairs work with one data set and build all three plots on graph paper, using the same number line scale for each. The data are the heights, in centimeters, of 16 tomato seedlings after four weeks:
Heights of 16 tomato seedlings in centimeters, ordered
Seedlings
Heights (cm)
1-8
18, 22, 25, 26, 27, 29, 30, 31
9-16
31, 33, 34, 36, 38, 40, 44, 51
Check each stage before pairs move on. Histogram with bins 10-19, 20-29, 30-39, 40-49, 50-59: frequencies 1, 5, 7, 2, 1. Box plot: median (31 + 31)/2 = 31, Q1 = (26 + 27)/2 = 26.5, Q3 = (36 + 38)/2 = 37, so the summary is 18, 26.5, 31, 37, 51. The dot plot has almost no stacks, which is a good moment to ask why a dot plot is less useful when nearly every value is different. Watch for these errors: an unevenly spaced number line, gaps between histogram bars, and a box plot drawn from the unordered list.
Independent Practice10-15 minutes
Students work alone on the resting heart rates, in beats per minute, of 15 students: 58, 62, 64, 65, 66, 68, 70, 71, 72, 72, 75, 78, 80, 84, 90. They draw a histogram with bins 50-59, 60-69, 70-79, 80-89, 90-99 (frequencies 1, 5, 6, 2, 1) and a box plot (summary 58, 65, 71, 78, 90), and then write one sentence about what each display shows best. Early finishers draw the dot plot as well and compare it with the histogram.
Closure5 minutes
Exit ticket: (1) A player scored 8, 11, 12, 14, 15, 15, 19, 21 and 26 points in 9 games. Find the five-number summary. (Answer: 8, 11.5, 15, 20, 26.) (2) Sketch the box plot above a number line from 5 to 30. (3) Name one thing a histogram shows that a box plot does not.
Differentiation Strategies
For Struggling Students
Give a pre-drawn number line and a bin table with the intervals already filled in, so students focus on placing values and counting
Have students cross off each value in the list as they plot or tally it, and check that the number of dots or the sum of the frequencies equals n
Use sticky notes for the five-number summary: students physically fold an ordered strip of values in half, then fold each half again
For Advanced Students
Ask for two different data sets of 9 values that have the same box plot but very different dot plots
Have students make histograms of one data set with three different bin widths and argue which width shows the data best
Ask students to find out how a spreadsheet or graphing tool computes quartiles and compare its results with the split-the-halves method on an even-sized data set
Assessment Guidance
What to Look For
Check that every display sits on an evenly scaled number line: an uneven scale is the error that makes a histogram or box plot misleading even when the numbers are right. In histograms, look for bins of equal width that cover the data with no gaps or overlaps, and frequencies that add up to n. In box plots, check that students ordered the data first, handled the median correctly when n is odd, and drew the box and whiskers to scale rather than as equal-sized parts. Ask students to justify their choice of display in one sentence.
02
Classroom Activities
3 Activities
1
Human Dot Plot to Human Box Plot
20 minWhole class
Students become the data. They first form a dot plot on a number line taped to the floor, then re-form into an ordered line to find the five-number summary with their own bodies. The physical move from one display to the other shows what a box plot keeps and what it throws away.
Procedure
Tape a number line from 0 to 20 on the floor with masking tape, marking every whole number at equal steps
Each student writes the number of hours of sleep they got over the last two school nights, rounded to the nearest hour, on a sticky note
Students stand on their value; students with the same value line up one behind another to make a stack. Photograph the "human dot plot"
Students now form a single ordered line. The class finds the median person (or the pair in the middle), then the middle of each half. Those students hold up signs for Q1, median and Q3; the two ends hold signs for the minimum and maximum
Record the five-number summary and draw the box plot on the board above the same number line as the dot plot photo
Discussion Questions
How many students stand between the Q1 and Q3 sign holders? What fraction of the class is that?
Which students "disappear" when we switch to the box plot?
If one more student joined with a value of 20, which parts of the box plot could change?
Modification for Distance Learning
Use a shared slide with a number line and draggable dots. Each student drags one dot to their value; the teacher then copies the ordered values into a free graphing tool to show the box plot next to the dot plot.
2
Bin Width Experiment
20 minGroups of 3
Every group gets the same 30 values and each member draws a histogram with a different bin width. Comparing the three pictures shows that bin width is a choice the maker of a histogram makes, and that the choice changes what readers see.
Student 2 uses bins of width 10 starting at 10 (10-19, ..., 60-69). Frequencies: 4, 8, 8, 5, 3, 2
Student 3 uses bins of width 20 starting at 10 (10-29, 30-49, 50-69). Frequencies: 12, 13, 5
All three use the same horizontal scale from 10 to 70 so the drawings can be laid side by side
Each group checks that each set of frequencies adds up to 30
Discussion Questions
Which histogram shows the most detail? Which is easiest to read?
What feature of the data does the width-20 histogram hide?
If you had 3,000 runners instead of 30, would you choose narrower or wider bins? Why?
3
Match the Displays Card Sort
15-20 minPairs
Pairs receive 12 cards: 4 raw data sets, 4 box plot summaries and 4 histogram frequency lists, all shuffled. They match each data set with its box plot and its histogram, which requires them to compute and to reason about what each display keeps.
Cards
Data cards (9 values each): Set A 1, 2, 2, 3, 3, 3, 4, 4, 5. Set B 1, 1, 2, 2, 3, 5, 8, 10, 11. Set C 6, 8, 9, 9, 10, 10, 11, 11, 11. Set D 0, 2, 4, 5, 6, 7, 8, 10, 12
Box plot cards (five-number summaries): 0, 3, 6, 9, 12 and 1, 2, 3, 4, 5 and 6, 8.5, 10, 11, 11 and 1, 1.5, 3, 9, 11
Remove the data cards. Pairs must match only box plots to histograms and explain how, for example by checking which histogram has its lowest bar in the same place as a box plot's minimum. Then they sketch a dot plot that fits both cards.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Dot Plot and Its Box Plot on the Same Scale
The 11 puzzle times, 4, 6, 7, 7, 9, 10, 12, 13, 15, 18 and 22 minutes, drawn as a dot plot and as a box plot over identical number lines. Each quarter of the box plot holds 2 or 3 of the dots. The long right whisker matches the spread-out dots from 15 to 22.
Diagram 2: Histogram of Commute Times
Commute times of 20 students grouped into bins 0-9, 10-19, 20-29, 30-39 and 40-49 minutes. Bar heights are the counts 3, 7, 6, 3 and 1, drawn to scale.
04
Homework Assignment
~30 min
HSS.ID.A.1 Homework: Representing Data on a Number Line
Directions: Use graph paper and a ruler. Draw every display above an evenly scaled number line and label the axis with the variable and its units. Show the ordered list and your work for every five-number summary. Split the data in half for quartiles as in class, leaving the median out when there is an odd number of values.
Part 1: Dot Plots (Problems 1-2)
A soccer team scored these numbers of goals in 15 games: 0, 1, 1, 2, 0, 3, 1, 2, 2, 1, 4, 0, 1, 2, 6. Draw a dot plot. In how many games did the team score 2 or more goals? Which value sits apart from the rest?
Two data sets of 9 values are P: 2, 4, 4, 4, 6, 8, 8, 8, 10 and Q: 2, 4, 4, 5, 6, 7, 8, 8, 10. Draw a dot plot of each above the same scale, find the five-number summary of each, and draw both box plots. What do the dot plots show that the box plots hide?
Part 2: Histograms (Problems 3-4)
The battery life, in hours, of 18 phones on a full charge: 7.5, 8.2, 8.8, 9.1, 9.4, 9.9, 10.3, 10.5, 10.8, 11.0, 11.2, 11.6, 11.9, 12.4, 12.7, 13.5, 14.1, 15.8. Make a frequency table with the bins 7 to under 9, 9 to under 11, 11 to under 13, 13 to under 15 and 15 to under 17 hours, then draw the histogram.
A librarian recorded the minutes 40 students spent reading on one evening: 0-14 minutes: 6 students, 15-29: 11, 30-44: 13, 45-59: 7, 60-74: 3. Draw the histogram. (a) How many students read at least 45 minutes? (b) What percent of the students is that? (c) Which bin contains the median? (d) Can you tell the longest reading time exactly? Explain.
Part 3: Box Plots (Problems 5-6)
The weights, in pounds, of 13 students' backpacks: 6, 8, 9, 10, 11, 11, 12, 14, 15, 15, 17, 19, 24. Find the five-number summary and draw the box plot to scale.
A box plot of 60 test scores has the five-number summary 52, 68, 75, 84, 98. (a) Find the range and the IQR. (b) About how many scores are between 68 and 84? (c) About what percent of the scores are above 75? (d) Can you find the mean from this box plot? Explain.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Scale and Labels
Evenly scaled number line, axis labeled with variable and units
Scale even but labels missing, or one uneven interval
No number line or scale badly uneven
Dot Plots and Histograms
Every value plotted or counted once; bins equal and touching; totals checked
One counting or bin error
Several values missing or bins overlap
Five-Number Summaries and Box Plots
Correct summary from the ordered list; box plot drawn to scale
One quartile error or box not to scale
Summary missing or data not ordered
Reading and Choosing Displays
Correct readings with reasons tied to what each display shows
Correct readings, reasons missing
Readings incorrect
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again. Quartiles use the split-the-halves method from the lesson.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A dot plot of the number of pets owned by students in a class has 4 dots above 0, 6 dots above 1, 3 dots above 2 and 1 dot above 3. How many students are in the data set?
Answer: C
Each dot is one student, so add the stacks: 4 + 6 + 3 + 1 = 14. Choice B is the height of the tallest stack, not the number of students. Choice D leaves out the 4 students with 0 pets.
Question 2 of 20 · Multiple Choice
A histogram of the heights of club members uses the bins 150-159 cm, 160-169 cm, 170-179 cm and 180-189 cm. One member is exactly 160 cm tall. Which bar includes that height?
Answer: B
The bin 160-169 starts at 160, so a height of exactly 160 cm is counted there. Each value belongs to exactly one bin, so choice C would count one person twice. Choice D would lose a data value.
Question 3 of 20 · Multiple Choice
Which display lets you read off every individual value in a small data set?
Answer: A
A dot plot draws one dot per value at its exact place on the number line, so the full data list can be recovered. A histogram shows only how many values fall in each bin, and a box plot shows only five summary values, so choices B and C lose the individual values.
Question 4 of 20 · Multiple Choice
Find the five-number summary of 3, 5, 6, 8, 11, 12, 15.
Answer: D
The median of 7 ordered values is the 4th value, 8. Leave it out: Q1 is the median of 3, 5, 6, which is 5, and Q3 is the median of 11, 12, 15, which is 12. Choice A includes the median 8 in both halves, and choice B uses the values next to the median instead of the middle of each half.
Question 5 of 20 · Multiple Choice
What is the median of 14, 15, 17, 18, 20, 21, 23, 24, 26, 29?
Answer: B
There are 10 values, so the median is halfway between the 5th and 6th values: (20 + 21) / 2 = 20.5. Choices A and C pick only one of the two middle values. Choice D is the mean, 207 / 10, not the median.
Question 6 of 20 · Multiple Choice
For the same 10 values, 14, 15, 17, 18, 20, 21, 23, 24, 26, 29, what is the interquartile range (IQR = Q3 - Q1)?
Answer: C
The lower half is 14, 15, 17, 18, 20, so Q1 = 17. The upper half is 21, 23, 24, 26, 29, so Q3 = 24. IQR = 24 - 17 = 7. Choice A is the range, 29 - 14. Choice B subtracts Q1 from the median instead of from Q3.
Question 7 of 20 · Multiple Choice
About what fraction of the data values in a box plot lie between the left and right edges of the box?
Answer: A
The box runs from Q1 to Q3, and the quartiles split the ordered data into four groups of about the same size, so about half of the values are inside the box. Choice D confuses the length of the box with the number of values: a short box means the middle half is packed close together, not that it holds fewer values.
Question 8 of 20 · Multiple Choice
A box plot of monthly phone bills (dollars) has minimum 20, Q1 = 35, median 40, Q3 = 55 and maximum 90. Which statement is true?
Answer: D
Q3 = 55 means about 75% of the values are at or below 55, so about 25% are above it. Choice A is false: the left whisker is 35 - 20 = 15 dollars long and the right whisker is 90 - 55 = 35 dollars long. Choice B confuses Q3 with the median. Choice C is wrong because a box plot does not show the mean.
Question 9 of 20 · Multiple Choice
A histogram uses the bins 0-4, 5-9, 10-14 and 15-19, with frequencies 2, 5, 9 and 4. How many data values are 10 or greater?
Answer: C
The values 10 or greater are in the bins 10-14 and 15-19: 9 + 4 = 13. Choice B counts only one of those bins. Choice D is the total number of values, 2 + 5 + 9 + 4.
Question 10 of 20 · Multiple Choice
A survey asked 50 students four questions. Which answers should be displayed in a histogram rather than a bar graph?
Answer: B
A histogram needs a numerical variable that can be placed on a number line and grouped into intervals, such as minutes. The other three choices are categories with no numerical order, so they belong in a bar graph. Grouping minutes into bins such as 0-14, 15-29 and so on gives touching bars.
Question 11 of 20 · Multiple Choice
A sports scientist has the reaction times of 400 athletes. Which display is the least practical for these data?
Answer: A
With 400 values, a dot plot needs 400 dots and the stacks get too tall to read or draw. A histogram groups the values into bins, and a box plot needs only five numbers, so both handle large data sets well.
Question 12 of 20 · Multiple Choice
A teacher redraws a histogram of the same data with bins twice as wide. What usually happens?
Answer: D
Wider bins merge neighboring bins, so there are fewer, taller bars and small features such as gaps or a second peak can disappear. Choice A is false: the frequencies still add up to the number of data values. Choice B is false because only the grouping changes, not the data.
Question 13 of 20 · Multiple Choice
Which of these can you NOT find from a box plot alone?
Answer: B
A box plot of 12 values and a box plot of 1,200 values can look identical, because it shows only the minimum, Q1, median, Q3 and maximum. The median, the range (max - min) and the IQR (Q3 - Q1) can all be read from those five values.
Question 14 of 20 · Multiple Choice
A dot plot shows 2 dots above 1, 3 dots above 2, 5 dots above 3 and 1 dot above 4. What is the median?
Answer: C
There are 2 + 3 + 5 + 1 = 11 values, so the median is the 6th value in order. The first 5 values are 1, 1, 2, 2, 2, so the 6th value is 3. Choice D is the height of the tallest stack, not a data value. Choice A stops one value too early.
Question 15 of 20 · Short Answer
Make a frequency table with bins of width 5 (40-44, 45-49, 50-54, 55-59) for these 12 race finishing times in minutes: 41, 43, 44, 46, 47, 47, 49, 50, 52, 53, 55, 58. Then describe how the histogram would look.
40-44: 3, 45-49: 4, 50-54: 3, 55-59: 2 (total 12). The histogram has four touching bars, tallest in the 45-49 bin, and the heights fall off slowly to the right. Check that the frequencies add up to 12.
Question 16 of 20 · Short Answer
Find the five-number summary of 3, 4, 4, 6, 7, 8, 9, 9, 11, 12, 14, 20 and describe the box plot.
There are 12 values, so the median is (8 + 9) / 2 = 8.5. The lower half 3, 4, 4, 6, 7, 8 gives Q1 = (4 + 6) / 2 = 5, and the upper half 9, 9, 11, 12, 14, 20 gives Q3 = (11 + 12) / 2 = 11.5. Summary: 3, 5, 8.5, 11.5, 20. The box runs from 5 to 11.5 with a line at 8.5, the left whisker goes to 3 and the right whisker is much longer, reaching 20.
Question 17 of 20 · Short Answer
A box plot of the heights (inches) of a basketball roster has the five-number summary 68, 72, 75, 78, 83. Find the range and the IQR, and say what each one measures.
Range = 83 - 68 = 15 inches: the distance from the shortest to the tallest player. IQR = 78 - 72 = 6 inches: the width of the box, where the middle half of the players' heights lie.
Question 18 of 20 · Short Answer
A histogram of 20 values has the bins 0-9, 10-19, 20-29 and 30-39 with frequencies 4, 8, 5 and 3. Which bin contains the median? Can you find the median exactly from the histogram?
The median of 20 values is halfway between the 10th and 11th values. The first bin holds values 1-4 and the second holds values 5-12, so the median is in the 10-19 bin. You cannot find it exactly, because a histogram does not show where the values sit inside a bin.
Question 19 of 20 · Short Answer
Two schools each have 300 students who took the same reading test. A counselor wants one picture that compares the medians and the spread of the scores at a glance. Which display should she use, and why?
Two box plots drawn above one shared number line. Each needs only five numbers, so 300 values are not a problem, and side-by-side boxes make the medians, quartiles and ranges easy to compare. Two histograms with the same bins would also work and would show more of the shape, but dot plots of 300 values would be too crowded.
Question 20 of 20 · Short Answer
Draw a dot plot of the hours of volunteer work done by 10 students last month: 2, 3, 3, 4, 4, 4, 5, 6, 6, 10. Which value has the tallest stack, and which value sits far from the others?
Put a number line from 0 to 10 and stack one dot per student: 1 dot at 2, 2 at 3, 3 at 4, 1 at 5, 2 at 6 and 1 at 10. The tallest stack is at 4 hours (3 dots). The value 10 sits far from the rest, with a gap from 6 to 10.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSS.ID.A.1 mean?
HSS.ID.A.1 means students can show a set of numerical data on a number line as a dot plot, a histogram or a box plot. The code reads as High School Statistics (HSS), Interpreting Categorical and Quantitative Data (ID), cluster A, standard 1. The standard covers one variable at a time, such as test scores or heights, not relationships between two variables.
Is HSS.ID.A.1 taught in Algebra 1 or in a statistics course?
It is usually taught in Algebra I, in a unit on one-variable statistics, and reviewed at the start of a high school statistics course. Students first meet these three displays in grade 6 (6.SP.B.4). The high school standard expects accurate construction, correct quartiles for any size of data set, and a reasoned choice of display.
What is the difference between a histogram and a bar graph?
A histogram displays a numerical variable grouped into intervals, while a bar graph displays categories. In a histogram the horizontal axis is a number line and the order of the bins is fixed. In a bar graph of, say, favorite sports, the bars could be rearranged without changing the meaning. Students who draw a histogram with spaces between bars are often thinking of a bar graph.
How do you find the quartiles for a box plot?
Order the data, find the median, then find the median of each half. When the number of values is odd, the median itself belongs to neither half. For example, for 2, 5, 7, 8, 12 the median is 7, the lower half is 2, 5 and the upper half is 8, 12. Some spreadsheet functions use a different rule and give slightly different quartiles; that is a known difference between methods, not an error.
Where does a value that lands on a bin boundary go?
It goes in exactly one bin, and the class should agree on the rule before counting. A common convention, used in this lesson, is that each bin includes its left edge and excludes its right edge, so with bins of width 5 a value of 15 is counted in 15-19. For whole-number data, labeling bins as 10-14, 15-19 and so on makes the rule visible.
When should students use a dot plot, a histogram or a box plot?
Match the display to the data and the question. A dot plot is best for small data sets, roughly up to 30 or 40 values, where seeing every value matters. A histogram is best for larger data sets when the shape of the distribution matters. A box plot is best for a quick summary of the center and spread, and for putting several groups side by side on one scale.
How many bins should a histogram have?
There is no single correct number; a useful starting point is 5 to 10 bins of equal width with easy-to-read edges such as multiples of 5 or 10. Too few bins hide the shape; too many leave most bins with 0 or 1 value. Activity 2 has students compare three bin widths for the same data so they see the trade-off.
What are common mistakes when drawing box plots?
Three errors come up often: finding the median of the unordered list, drawing the four parts of the box plot as equal-sized pieces instead of to scale, and including the median in both halves when finding quartiles. A quick check helps: about a quarter of the data should lie in each whisker and in each half of the box.
How does HSS.ID.A.1 connect to later statistics standards?
HSS.ID.A.1 is the starting point of the cluster. HSS.ID.A.2 uses the displays to choose and compare measures of center and spread, and HSS.ID.A.3 interprets differences in shape, center and spread, including outliers. Later, HSS.ID.A.4 fits data to a normal distribution, and a histogram is how students judge whether that fit is reasonable.
Should students draw these displays by hand or with technology?
Both, in that order. Drawing a few displays by hand teaches what each mark means, including how bins and quartiles are chosen. After that, a graphing calculator or free online tool is the practical choice for large data sets. When technology is used, ask students to state the bin width and the quartile method the tool used.
07
Related Standards
6 standards
These standards connect to HSS.ID.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.SP.B.4Prerequisite
Display numerical data in dot plots, histograms and box plots on a number line
