6.SP.B.4Common CoreMathStatistics and ProbabilityGrade 6
6.SP.B.4: Dot Plots, Histograms and Box Plots
In plain English: 6.SP.B.4 is the Common Core grade 6 math standard that asks students to display numerical data on a number line with dot plots, histograms and box plots. Students choose a scale, draw each plot to scale, and find the five-number summary (minimum, quartiles, median, maximum) that a box plot needs. It prepares for comparing data sets in grade 7 statistics.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Common Core State Standards for Mathematics · Domain: Statistics and Probability (SP) · Cluster: Summarize and describe distributions. Also written as 6.SP.4 · Official standard
Students learn three ways to show numerical data (data that are numbers from counting or measuring) on a number line. In a dot plot, each data value is one dot above its place on the number line. In a histogram, the number line is split into equal intervals called bins, and the height of each bar shows how many values fall in that bin. In a box plot, five numbers called the five-number summary are marked: the smallest value (the minimum), the lower quartile (the middle of the lower half of the data), the median (the middle value), the upper quartile (the middle of the upper half) and the largest value (the maximum). They are marked on the number line and joined by a box and two lines called whiskers.
Every plot is drawn to scale: equal distances on the number line stand for equal amounts. Students choose a scale that fits the data, build each plot from a list of values, and talk about what each plot shows well and what it hides. A dot plot keeps every value, a histogram shows the shape of a large data set, and a box plot shows where each quarter of the data lies. All data sets on this page are invented for teaching, with realistic values for grade 6 students.
Learning Objectives
By the end of this lesson, students will be able to:
Choose a number line scale that fits a data set and mark equal steps for equal amounts
Draw a dot plot of a data set, with one dot for each value
Sort data into equal bins and draw a histogram with correct bar heights
Find the five-number summary of a data set and draw a box plot to scale
Explain what each display shows clearly and what it hides
Prior Knowledge Required
Students should already be comfortable with:
Making line plots of measurement data 3.MD.B.45.MD.B.2
Placing whole numbers, fractions and decimals on a number line 6.NS.C.6
Knowing that data from a statistical question (a question that expects answers to vary) have a distribution, a way the values are spread out 6.SP.A.2
Adding and dividing decimals, for example finding the number halfway between 9 and 10 6.NS.B.3
Write this invented list on the board: the hours of sleep that 15 students reported for last night.
Warm-Up Prompt
"Here are 15 sleep times in hours: 9, 8, 10, 9, 7, 9, 8, 11, 9, 10, 8, 9, 7.5, 10, 8.5. Without adding anything up, what is a typical amount of sleep for this group? How could you draw these numbers so the answer jumps out?"
Let pairs sketch any picture for two minutes, then share. Many students will list the numbers in order or make tally marks. Point out that 9 hours shows up 5 times, more than any other value, and that the values run from 7 to 11 hours. Say that today they will learn three standard pictures of data, all drawn on a number line: the dot plot, the histogram and the box plot. Ask one student to draw a number line from 7 to 11 with a mark every half hour, and have the class place one dot per student. That picture is already a dot plot.
Direct Instruction20-25 minutes
Part 1: Dot plots. A dot plot is a number line with one dot above the matching value for each observation (one data value, such as one student's measurement). Steps: find the smallest and largest values, draw a number line that covers them with equal steps, and stack one dot per value. Equal spacing matters: 15 to 16 must be the same distance as 20 to 21. Work Example 1 with Diagram 1 (top).
Dot plot
Twenty students measured their hand span (the distance from the tip of the thumb to the tip of the little finger, with the hand spread) to the nearest centimeter. Invented data: 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 21.
Equation: Number line from 14 to 22 cm, one step per centimeter; stacks of 1, 3, 4, 6, 4, 1, 1 dots above 15 to 21; the tallest stack is at 18 cm, and 17 of the 20 dots are between 16 and 19 cm
Histogram
The heights of 25 students, to the nearest centimeter (invented data): 136, 139, 141, 142, 143, 143, 145, 146, 146, 147, 148, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 158, 159, 161, 164. Use bins 5 cm wide, starting at 135.
Equation: Bins 135 up to 140, 140 up to 145, and so on to 160 up to 165 hold 2, 4, 7, 6, 4 and 2 students; the tallest bar is 145 up to 150, and 12 students are 150 cm or taller
Box plot, odd number of values
A school basketball team scored these points in 11 games (invented data): 24, 29, 31, 33, 36, 38, 38, 41, 44, 47, 55.
Part 2: Histograms. When a data set has many different values, a dot plot gets long and flat. A histogram groups the values into bins: equal intervals on the number line, such as 145 up to 150 centimeters. The frequency of a bin (how many values fall in it) is the height of its bar. Bars touch, because the bins cover the number line with no gaps. Agree on a rule for values on an edge: in this lesson a bin includes its left number and not its right one, so 150 goes in the bin 150 up to 155. Work Example 2 with Diagram 1 (bottom). Ask: can you tell from the histogram alone how tall the tallest student is? (No. You only know that the tallest student is somewhere from 160 up to 165 cm.)
Part 3: Box plots. Recall the median: the middle value when the data are listed in order, or the number halfway between the two middle values when the count is even. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half. When the count is odd, leave the median itself out of both halves. Together with the minimum (smallest value) and maximum (largest value), these make the five-number summary. To draw a box plot, mark the five numbers above a number line, draw a box from Q1 to Q3 with a line inside at the median, and draw whiskers (lines) from the box out to the minimum and to the maximum. The four parts (left whisker, two parts of the box, right whisker) each hold about one quarter of the data. The whole plot stretches across the range (the maximum minus the minimum). Diagram 2 shows Example 3 as a dot plot above a box plot on the same scale. Work Example 4 on the board, and point out that Q1 and Q3 can be halfway between two values.
Part 4: Choosing a display. A dot plot shows every value and works best for small data sets. A histogram shows the shape of a large data set but hides the exact values. A box plot shows the center and the spread of each quarter, but it hides how many values there are and does not show the mean (the sum of the values divided by how many values there are).
Guided Practice15 minutes
Pairs build two displays of the same invented data set on grid paper. The teacher circulates and checks each scale before students draw.
Push-ups completed in 30 seconds by 16 students (invented data), in order
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Push-ups
12
15
16
18
18
20
21
21
22
24
25
25
27
29
31
34
Step 1: make a histogram with bins 5 push-ups wide, starting at 10 (10 up to 15, 15 up to 20, and so on). The bar heights are 1, 4, 5, 4 and 2. Step 2: find the five-number summary. With 16 values, the median is halfway between the 8th and 9th values: (21 + 22) ÷ 2 = 21.5. The lower half (first 8 values) has middle values 18 and 18, so Q1 = 18. The upper half has middle values 25 and 27, so Q3 = 26. The summary is 12, 18, 21.5, 26, 34. Step 3: draw the box plot above a number line from 10 to 35 with a mark every 5. Ask pairs to hold their two displays side by side: both show that most students did from 15 to 30 push-ups, but only the box plot shows where the middle half of the students fall. Watch for pairs who draw bars with gaps between them or who space the number line unevenly.
Independent Practice10-15 minutes
Each student works alone on one invented data set: the number of books 15 students read over the summer, which are 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 6, 8, 12. (1) Draw a dot plot on a number line from 0 to 12. (The tallest stack is at 3 books, with 4 dots.) (2) Find the five-number summary. (Minimum 0, Q1 = 2, median = 8th value = 3, Q3 = 5, maximum 12.) (3) Draw a box plot on the same scale, just below the dot plot. (4) Write one sentence about what the dot plot shows that the box plot does not. (For example: the dot plot shows that 3 students read 2 books; the box plot cannot show how many students read any one number of books.)
Closure5 minutes
Exit ticket: (1) A data set has the five-number summary 4, 7, 9, 12, 20. Sketch its box plot on a number line from 0 to 20. Which of the four parts is longest? (The right whisker, from 12 to 20, is 8 units long.) (2) A school nurse has the heights of 150 students. Which display would you pick to show the shape of the data, and why? (A histogram, because 150 dots would be hard to draw and read.) Collect the tickets and sort them by whether the box plot was drawn to scale.
Differentiation Strategies
For Struggling Students
Give a number line already marked with equal steps, so students focus on placing the dots or bars
Have students write the data in order on a strip of paper, then fold the strip in half to find the median and fold each half again to find Q1 and Q3
Start with data sets of 7 or 8 values before moving to 15 or more
For Advanced Students
Give a five-number summary and ask students to invent a data set of 9 values that has it, then check it with another student
Ask students to draw the same data as histograms with two different bin widths and write which one tells the story better
Ask how the box plot changes if the largest value in Example 3 changes from 55 to 75, and which parts of the plot stay the same
Assessment Guidance
What to Look For
Check that every number line uses equal steps and covers the smallest and largest values. In dot plots, look for one dot per observation and neat stacks. In histograms, check that the bins are equal in width, that the bars touch, and that edge values follow the class rule. In box plots, check that students order the data first, find the median correctly for odd and even counts, leave the median out of the halves when the count is odd, and draw the box and whiskers to scale rather than making every part the same length.
02
Classroom Activities
3 Activities
1
Measure and Plot: A Class Dot Plot
15 minPairs, then whole class
Pairs measure each other's hand span in centimeters, and the class builds one large dot plot with sticky notes on a number line on the board.
Procedure
One partner spreads a hand flat on the desk. The other measures from the tip of the thumb to the tip of the little finger with a centimeter ruler and rounds to the nearest centimeter
Switch roles, then each student writes the value on a sticky note
A student volunteer draws a number line from 14 to 22 cm on the board with equal steps. Hand spans of students aged 11-12 usually fall in this range; extend the line if a value falls outside it
Students place their sticky notes above their values, stacking notes of the same value in neat columns so each note is one dot
Discussion Questions
How many observations are on the plot? Does it match the number of students here today?
Where is the tallest stack? Is it near the middle of the plot or near one end?
Why must the notes in a stack be the same size and evenly spaced?
What would change if we measured to the nearest half centimeter instead?
Modification for Distance Learning
Students measure their own hand span at home and type the value into a shared spreadsheet. The teacher builds the dot plot live on a shared grid slide while students watch and check each dot.
2
Histogram Bin Challenge
20 minGroups of 3
Every group gets the same data card, but groups use different bin widths. Then groups compare their histograms and decide which bin width tells the clearest story.
Data Card: Standing Long Jump (24 students, invented data, in centimeters)
Pairs find the five-number summary of each data card and match it to a summary card
On one number line from 0 to 20, pairs draw all four box plots, one above the other
Discussion Questions
All four cards have the same minimum and maximum. Why do the box plots still look different?
Which cards have a median of 11? (Cards 1, 2 and 4)
Card 2 and card 3 have the same Q3. Which one has the wider box, and what does that tell you? (Card 2: its box runs from 6 to 16, and the box of card 3 runs from 9 to 16, so the middle half of card 2 is more spread out)
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Dot Plot and a Histogram
Top: a dot plot of 20 hand spans (Example 1). Each dot is one student, and the tallest stack is at 18 cm. Bottom: a histogram of 25 heights (Example 2), with bins 5 cm wide. Each bar shows how many students fall in its bin; the tallest bar is 145 up to 150 cm. Both are drawn to scale on a number line.
Diagram 2: From a Dot Plot to a Box Plot
The 11 game scores from Example 3 as a dot plot (top) and a box plot (bottom) on the same scale. The dashed lines carry the five-number summary down to the box plot: minimum 24, Q1 = 31, median 38, Q3 = 44 and maximum 55. The long right whisker shows that the top quarter of the scores is more spread out.
04
Homework Assignment
~30 min
6.SP.B.4 Homework: Dot Plots, Histograms and Box Plots
Directions: Use grid paper or a ruler. Every number line must have equal steps and a label with the units. List the data in order before you find any median or quartile.
Part 1: Dot Plots (Problems 1-2)
The number of minutes a school bus arrived late on 16 school days (invented data): 0, 2, 1, 0, 3, 5, 1, 0, 2, 2, 1, 1, 4, 1, 19, 2. Draw a dot plot on a number line from 0 to 20. Which value has the tallest stack? Which value stands apart from the rest, and what might explain it?
A class measured 12 bean seedlings to the nearest half centimeter after 10 days (invented data): 4, 4.5, 5, 5, 5.5, 5.5, 5.5, 6, 6, 6.5, 7, 8. Draw a dot plot with a mark every 0.5 cm. How many seedlings are taller than 5.5 cm?
Part 2: Histograms (Problems 3-4)
The number of minutes 20 students spent reading on Saturday (invented data): 0, 5, 10, 15, 15, 20, 20, 25, 30, 30, 30, 35, 40, 45, 45, 50, 60, 60, 75, 90. Make a histogram with bins 15 minutes wide, starting at 0 (0 up to 15, 15 up to 30, and so on). How many students read for 45 minutes or more?
A histogram of the daily high temperatures in a town for the 30 days of June (invented data) has these bars: 70 up to 75 °F: 3 days; 75 up to 80 °F: 8 days; 80 up to 85 °F: 11 days; 85 up to 90 °F: 6 days; 90 up to 95 °F: 2 days. Draw the histogram. On how many days was the high at least 80 °F? Can you tell the hottest temperature of the month from the histogram? Explain.
Part 3: Box Plots (Problems 5-6)
The number of pages in 13 chapter books on a classroom shelf (invented data): 88, 104, 120, 132, 146, 150, 168, 184, 190, 212, 236, 250, 310. Find the five-number summary and draw a box plot on a number line from 80 to 320 with a mark every 20 pages.
The number of minutes 10 students waited in the lunch line (invented data): 2, 3, 3, 4, 5, 6, 6, 7, 9, 14. Draw a dot plot and a box plot on the same number line from 0 to 15. Name one thing the dot plot shows that the box plot does not, and one thing the box plot shows more clearly.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Number Line Scale
Equal steps, labeled with units, covers all values
Scale mostly correct with one uneven step or missing label
Uneven or missing scale
Dot Plots
One dot per value, neat stacks, questions answered
One or two dots missing or misplaced
Dots do not match the data
Histograms
Equal bins, correct bar heights, touching bars
One bar height wrong or bars with gaps
Bins unequal or heights wrong
Box Plots
Correct five-number summary, drawn to scale
One summary value wrong or plot not to scale
Summary missing or plot missing
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. Every data set in the quiz is invented.
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
In a dot plot, what does each dot stand for?
Answer: A
Each dot is one observation, so a data set of 20 values has 20 dots. Choice B mixes up a dot with a total: a dot plot never adds values together. Choice C describes the median, which a dot plot does not mark. Choice D is the count of all the dots, not what one dot means.
Question 2 of 20 · Multiple Choice
Twelve students listed how many pets they have (invented data): 0, 1, 1, 2, 0, 3, 1, 2, 1, 0, 4, 1. In a dot plot of these data, how many dots are above 1?
Answer: C
Five students have exactly 1 pet, so the stack above 1 has 5 dots. Choice A counts the students with 0 pets. Choice B is every dot on the plot. Choice D counts the students with 2 pets.
Question 3 of 20 · Multiple Choice
A dot plot shows the goals a soccer team scored in each game of its season: 2 dots above 0, 4 dots above 1, 6 dots above 2, 3 dots above 3 and 1 dot above 7. How many games did the team play?
Answer: B
Each dot is one game, so add the stacks: 2 + 4 + 6 + 3 + 1 = 16 games. Choice A counts the stacks instead of the dots. Choice C is the largest number of goals in one game. Choice D is the height of the tallest stack.
Question 4 of 20 · Multiple Choice
Aiden's data run from 12 to 27. Which number line is set up correctly for a dot plot of his data?
Answer: D
A number line must use equal steps for equal amounts and cover every value, so marks every 1 from 10 to 30, equally spaced, work. Choice A spaces steps of 3, 5 and 7 the same distance apart, so the plot is not to scale. Choice B changes the step size partway along the line. Choice C leaves out the numbers between data values, which hides the gaps in the data.
Question 5 of 20 · Multiple Choice
A histogram of the ages of people at a pool uses the bins 0 up to 10, 10 up to 20, 20 up to 30, and so on. Each bin includes its left number but not its right one. In which bar is a 20-year-old counted?
Answer: B
The bin 20 up to 30 includes its left edge, 20, so a 20-year-old is counted there. Choice A counts the edge value in the lower bin, the reverse of the rule. Choice C counts one person twice, so the bar heights would add up to more than the number of people. Choice D leaves the person out of the histogram.
Question 6 of 20 · Multiple Choice
Fifteen students took a 50-point quiz (invented data): 28, 31, 35, 36, 38, 40, 40, 41, 43, 44, 45, 46, 48, 49, 50. In a histogram with bins 30 up to 40, 40 up to 50 and so on, how tall is the bar for 30 up to 40?
Answer: D
The scores 31, 35, 36 and 38 are at least 30 and less than 40, so the bar is 4 tall. Choice A also counts the two scores of 40, which belong in the next bin. Choice B is the height of the bar for 40 up to 50. Choice C counts every student.
Question 7 of 20 · Multiple Choice
Which question can you NOT answer from a histogram alone?
Answer: B
A histogram groups values into bins, so it shows only the bin that holds the largest value, not the value itself. Choice A can be answered: the tallest bar shows the bin with the most values. Choice C can be answered roughly by finding where half of the bar heights are on each side. Choice D is the height of that bar.
Question 8 of 20 · Multiple Choice
A histogram shows the heights of 30 tomato plants (invented data): 100 up to 120 cm: 4 plants; 120 up to 140 cm: 9 plants; 140 up to 160 cm: 11 plants; 160 up to 180 cm: 6 plants. How many plants are at least 140 cm tall?
Answer: C
Plants at least 140 cm tall are in the last two bars: 11 + 6 = 17 plants. Choice A uses only the bar for 140 up to 160 and forgets the tallest plants. Choice B adds the bars from 120 cm up. Choice D counts the plants shorter than 140 cm.
Question 9 of 20 · Multiple Choice
Nine students recorded how many minutes they spent on a science quiz (invented data): 12, 15, 16, 18, 20, 21, 25, 26, 30. What are the lower quartile (Q1) and upper quartile (Q3)?
Answer: C
The median is the 5th value, 20. Leave it out: the lower half is 12, 15, 16, 18, whose middle is (15 + 16) ÷ 2 = 15.5, and the upper half is 21, 25, 26, 30, whose middle is (25 + 26) ÷ 2 = 25.5. Choice A gives the minimum and maximum. Choice B gives the two values next to the median. Choice D takes the 2nd value and the 2nd-to-last value instead of the middle of each half.
Question 10 of 20 · Multiple Choice
Ten students recorded how many minutes they practiced piano one week (invented data): 20, 25, 25, 30, 35, 45, 50, 55, 60, 75. Which five-number summary should you use to draw the box plot?
Answer: A
The median is (35 + 45) ÷ 2 = 40. The lower half 20, 25, 25, 30, 35 has middle value 25, and the upper half 45, 50, 55, 60, 75 has middle value 55. With the minimum 20 and maximum 75, the summary is 20, 25, 40, 55, 75. Choice B uses the 4th and 7th values, 30 and 50, as the quartiles. Choice C uses the mean, 420 ÷ 10 = 42, in place of the median. Choice D stops at 60 and leaves out the largest value, 75.
Question 11 of 20 · Multiple Choice
In a box plot, the box goes from 18 to 30. About what fraction of the data values are from 18 to 30?
Answer: B
The box runs from Q1 to Q3. One quarter of the data is between Q1 and the median, and another quarter is between the median and Q3, so the box holds about half. Choice A counts only one part of the box. Choice C adds a whisker to the box. Choice D forgets the values on the whiskers.
Question 12 of 20 · Multiple Choice
A box plot has a minimum of 10, Q1 = 18, median 22, Q3 = 30 and a maximum of 45. What does the long right whisker tell you?
Answer: A
Each whisker holds about a quarter of the data. The right whisker runs 45 - 30 = 15 units and the left whisker 18 - 10 = 8 units, so the top quarter is more spread out. Choice B confuses length with count: both whiskers hold about the same number of values. Choice C cannot be read from a box plot. Choice D is false: 22 is 12 from the minimum and 23 from the maximum.
Question 13 of 20 · Multiple Choice
A class wants a display that shows every single value in a data set of 18 test scores. Which display should it choose?
Answer: C
A dot plot keeps each value as its own dot, and 18 values are few enough to draw. Choice A is wrong because a box plot shows only five numbers. Choice B is wrong because a histogram shows how many values are in each bin, not the values. Choice D is wrong because only the dot plot shows every value.
Question 14 of 20 · Multiple Choice
Which of these can you NOT find from a box plot alone?
Answer: D
A box plot shows the five-number summary but not how many values were used: a box plot of 9 values and a box plot of 900 values can look the same. Choice A is the line inside the box. Choice B is the end of the right whisker. Choice C is the maximum minus the minimum, the two ends of the whiskers.
Question 15 of 20 · Short Answer
Fourteen students recorded how many hours they volunteered last month (invented data): 2, 4, 3, 2, 5, 2, 6, 3, 2, 4, 3, 10, 2, 3. Draw a dot plot. Where is the tallest stack, and which value stands apart?
Draw a number line from 0 to 10 with a mark every 1 hour. The stacks are 5 dots above 2, 4 dots above 3, 2 dots above 4 and 1 dot each above 5, 6 and 10, for 14 dots in all. The tallest stack is at 2 hours, and 10 hours stands apart, 4 hours past the next value. A common error is to leave out the empty space between 6 and 10, which hides the gap.
Question 16 of 20 · Short Answer
Sixteen students weighed their backpacks in pounds (invented data): 6, 8, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 18, 19, 23. Give the bar heights for a histogram with bins 5 up to 10, 10 up to 15, 15 up to 20 and 20 up to 25.
Count the values in each bin, with each bin including its left number: 3, 8, 4 and 1. The bar heights add up to 16, one for each backpack. A common error is to put 10 and 15 in the lower bin, which gives 4, 8, 3 and 1.
Question 17 of 20 · Short Answer
A basketball player scored these points in 12 games (invented data): 4, 6, 7, 8, 8, 10, 12, 12, 14, 15, 18, 22. Find the five-number summary.
The data are already in order. With 12 values, the median is halfway between the 6th and 7th values: (10 + 12) ÷ 2 = 11. The lower half 4, 6, 7, 8, 8, 10 gives Q1 = (7 + 8) ÷ 2 = 7.5, and the upper half 12, 12, 14, 15, 18, 22 gives Q3 = (14 + 15) ÷ 2 = 14.5. The five-number summary is 4, 7.5, 11, 14.5, 22.
Question 18 of 20 · Short Answer
The daily high temperatures (°F) in a city for one week in March were (invented data): 52, 48, 55, 61, 50, 58, 57. Find the five-number summary and describe how to draw the box plot.
In order: 48, 50, 52, 55, 57, 58, 61. The median is the 4th value, 55. The lower half 48, 50, 52 gives Q1 = 50, and the upper half 57, 58, 61 gives Q3 = 58. The summary is 48, 50, 55, 58, 61. Draw a number line from 45 to 65, a box from 50 to 58 with a line at 55, and whiskers out to 48 and 61. A common error is to find the median before putting the values in order, which gives 61, the 4th value in the original list.
Question 19 of 20 · Short Answer
A coach has the 200-meter run times of 200 students. Explain why a histogram is a better choice than a dot plot for these data.
A dot plot needs one dot per value, so it would need 200 dots, and with many different times most stacks would be only one or two dots high. A histogram groups the times into equal bins, such as 30 up to 35 seconds, so a few bars show the shape of the data: where most times fall and how far they spread. The cost is that the exact times are hidden.
Question 20 of 20 · Short Answer
A student draws a box plot for the five-number summary 10, 14, 16, 25, 30 and makes the two parts of the box the same length. What went wrong?
A box plot must be drawn to scale on a number line. The left part of the box runs from 14 to 16, which is 2 units, and the right part runs from 16 to 25, which is 9 units. So the right part should be 4.5 times as long as the left part. Drawing them the same length hides that the values from 16 to 25 are much more spread out.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.SP.B.4 mean?
6.SP.B.4 means students can show numerical data on a number line in three ways: dot plots, histograms and box plots. They choose a scale with equal steps, draw each plot to scale from a list of data, and read what each plot shows. Finding the five-number summary for a box plot is part of the work.
Is 6.SP.B.4 a grade 6 or grade 7 standard?
It is a grade 6 standard in the Statistics and Probability domain. In grade 7, students use these same displays to compare two data sets (7.SP.B.3), and in high school they use them again to compare shape, center and spread (HSS.ID.A.1).
What is the difference between a dot plot and a line plot?
They are the same kind of display. Earlier grades often say "line plot" and use Xs; grade 6 usually says "dot plot" and uses dots. In both, each mark is one data value above its place on a number line.
How is a histogram different from a bar graph?
A histogram shows numerical data grouped into equal intervals on a number line, so its bars touch and their order is fixed. A bar graph shows categories, such as favorite fruits, so its bars have gaps and could be put in any order.
How do students choose the bin width for a histogram?
A good bin width gives about 5 to 10 bars. Too few bins hide the shape, and too many bins make lots of short bars. Friendly widths such as 2, 5, 10 or 20 make the scale easy to read. Students should also agree on where an edge value goes, for example that 40 belongs in the bin 40 up to 50.
How do you find the quartiles for a box plot in grade 6?
Put the data in order and find the median. The lower quartile is the median of the values below it, and the upper quartile is the median of the values above it. When the count is odd, leave the median out of both halves. Some calculators and spreadsheets use a slightly different rule and can give quartiles that differ a little, so tell students which rule the class uses.
What are common mistakes with these plots?
A common mistake is a number line with uneven steps, such as marks at 5, 10, 20 and 40 spaced the same distance apart. Others are histogram bars with gaps, finding the median before putting the data in order, and drawing every part of a box plot the same length. Checking the scale first catches many of these.
Why does a box plot not show the mean?
A box plot is built from the five-number summary, which uses only the order of the values: the minimum, the quartiles, the median and the maximum. The mean uses the sizes of all the values, so it is a different measure. Finding and choosing measures such as the mean and median is the work of the next standard, 6.SP.B.5.
Can students use technology to make these plots?
Yes, once they can draw each plot by hand. Free online graphing tools and spreadsheets can make dot plots, histograms and box plots quickly. Drawing a few by hand first helps students understand why the scale must be even and what each part of a box plot means.
How can parents help with 6.SP.B.4 at home?
Collect a small set of family data, such as the minutes each person spends getting ready in the morning for a week. Ask your child to draw a dot plot of it, then to find the median and the largest and smallest values. Ask what a typical morning looks like and which day stands out.
07
Related Standards
6 standards
These standards connect to 6.SP.B.4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
5.MD.B.2Prerequisite
Make a line plot of measurements in fractions of a unit and solve problems with it
Lesson coming soon
6.SP.A.2Prerequisite
Understand that data have a distribution described by its center, spread and shape
