6.SP.A.2Common CoreMathStatistics and ProbabilityGrade 6
6.SP.A.2: Describing a Distribution by Its Center, Spread and Shape
In plain English: 6.SP.A.2 is the Common Core grade 6 math standard that asks students to understand that data collected to answer a statistical question (one that expects different answers) has a distribution: the pattern of which values occur and how often. Students describe it by its center (a typical value), its spread (how far the values vary) and its overall shape, such as one peak in the middle or a long tail on one side.
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Common Core State Standards for Mathematics · Domain: Statistics and Probability (SP) · Cluster: Develop understanding of statistical variability. Also written as 6.SP.2 · Official standard
A statistical question is a question that expects different answers, such as "How many hours do sixth graders sleep on a school night?" The answers form a data set (a collection of values). Because the values differ, the data set has a distribution: the pattern of which values occur and how often each one occurs. In this lesson, students learn that every distribution can be described in three ways: its center (one typical value near the middle of the data), its spread (how far apart the values are) and its overall shape (the picture the data makes, such as one peak in the middle or a long tail on one side).
Students show data on a dot plot (a number line with one dot for each value, stacked when values repeat, like the line plots from grade 5). They use the median as a first measure of center and the range as a first measure of spread, and they learn the words for shape: symmetric, skewed, peak, cluster, gap and outlier. The focus is on describing and comparing distributions in words. Other measures of center and spread, and choosing among them, come later in 6.SP.A.3 and 6.SP.B.5. All data sets on this page are invented for teaching, and each one is labeled as invented.
Learning Objectives
By the end of this lesson, students will be able to:
Explain that the answers to a statistical question form a distribution, and show it on a dot plot
Describe the center of a distribution with a typical value such as the median
Describe the spread of a distribution with the range and with words like tightly grouped or spread out
Describe the overall shape of a distribution: symmetric, skewed left or right, one peak or two clusters, gaps and outliers
Compare two distributions by their center, spread and shape
Prior Knowledge Required
Students should already be comfortable with:
Recognizing statistical questions, which expect variability (different answers) 6.SP.A.1
Making a line plot of measurement data 5.MD.B.2
Ordering whole numbers and decimals and placing them on a number line 6.NS.C.7
Finding the number halfway between two numbers, such as 5 and 6
Write the question on the board and give each student one sticky note:
Warm-Up Prompt
"About how many minutes did it take you to get to school this morning? Write your answer on the sticky note. Before we put the notes up, predict: will most of us have the same answer? What might the smallest and largest answers be?"
Tape a number line from 0 to 40 minutes on the board and have students place their notes above their value, stacking notes that repeat. Point out that this is a statistical question (a question that expects different answers), so the answers vary. The picture on the board is the distribution of the class's answers. Ask three questions and write the students' words next to each: "What is a typical time for our class?" (center), "How different are the times?" (spread) and "What does the pile look like?" (shape). Keep the sticky notes up for the closure.
Direct Instruction20 minutes
Part 1: Center. The center of a distribution is one number that tells a typical value. The first measure of center students use is the median: put the values in order and take the middle one. With an even number of values, the median is halfway between the two middle values. Use Diagram 1: the 15 sleep times in order put the 8th value, 9 hours, in the middle.
Part 2: Spread. The spread tells how far apart the values are. A simple measure of spread is the range: the largest value minus the smallest value. Words help too: values can be tightly grouped (close together) or spread out. Two distributions can have the same center and very different spreads, as in the second example below.
Part 3: Overall shape. Teach the shape words with Diagram 2. A peak is a place where many dots pile up. A distribution is symmetric when the left half and the right half look about like mirror images. It is skewed right when most values are low and a long tail (a thin trail of dots) stretches to the right, and skewed left when the tail stretches to the left. A cluster is a group of values close together, a gap is an empty stretch of the number line with no values, and an outlier is a value far away from the rest of the data.
Describing one distribution
Invented data: hours of sleep on a school night for 15 sixth graders, to the nearest half hour: 6.5, 7.5, 8, 8, 8.5, 8.5, 8.5, 9, 9, 9, 9, 9.5, 9.5, 10, 10.5 (Diagram 1).
Equation: Center: the median is the 8th value, 9 hours. Spread: range = 10.5 - 6.5 = 4 hours, and most students sleep 8 to 9.5 hours. Shape: one peak at 9 hours and fairly symmetric, with the 6.5 a little apart from the rest
Equation: Both medians are 28, halfway between the 5th and 6th values. Group A's range is 32 - 23 = 9 and Group B's is 41 - 15 = 26, so Group B is much more spread out
Equation: Center: the median is halfway between the 10th and 11th values, (3 + 3) ÷ 2 = 3 books. Spread: range = 15 - 0 = 15 books. Shape: skewed right, with a peak at 2 books and a long tail toward 15
Two clusters
Invented data: minutes to finish a 1-mile fun run for 16 people, some running and some walking: 8, 9, 9, 10, 10, 11, 12, 16, 17, 18, 18, 19, 20, 21, 22, 24 (Diagram 2).
Equation: Shape: two clusters (8 to 12 minutes and 16 to 24 minutes) with a gap from 12 to 16. The median is (16 + 17) ÷ 2 = 16.5 minutes, which sits at the edge of the gap and describes neither group well
After the fourth example, ask: "Why is one number not enough here?" The runners and walkers form two groups, so a good description names both clusters. This is why the standard asks for center, spread and shape: each one tells something the others miss.
Guided Practice15 minutes
Pairs work on one data set together. They draw a dot plot on grid paper, then write one sentence each for center, spread and shape. One pair shares each sentence with the class.
Invented data: number of letters in the first names of 18 students in one class.
Letters
3
4
5
6
7
8
9
11
Number of students
1
3
5
4
2
1
1
1
Answers: center: with 18 values, the median is halfway between the 9th and 10th values, (5 + 6) ÷ 2 = 5.5 letters. Spread: range = 11 - 3 = 8 letters, but most names have 4 to 6 letters. Shape: one peak at 5 letters and a tail to the right (skewed right). The name with 11 letters is set apart by a gap at 10, so students may call it an outlier. Listen for pairs who find the middle of the column labels (3 to 11) instead of the middle of the 18 values: the median counts students, not columns.
Independent Practice10 minutes
Students describe two invented data sets on their own, with a dot plot for each. (1) Ages, in years, of the 12 people at a toddler swim class, where each child comes with one parent: 1, 2, 2, 2, 3, 3, 27, 31, 33, 35, 38, 41. (Two clusters: children 1 to 3 and parents 27 to 41, with a large gap. The median is (3 + 27) ÷ 2 = 15 years, an age nobody in the class has, so the description should name both clusters. Range = 41 - 1 = 40 years.) (2) Daily high temperatures, in degrees Fahrenheit, for 14 spring days in one town: 68, 70, 71, 71, 72, 72, 73, 73, 73, 74, 75, 75, 77, 79. (Median (73 + 73) ÷ 2 = 73 °F, range = 79 - 68 = 11 °F, one peak at 73 and roughly symmetric, a little longer on the right.)
Closure5 minutes
Go back to the sticky-note plot from the warm-up and have students write three sentences about it: one for center, one for spread, one for shape. Then give this exit ticket: invented data for 9 students, minutes to walk to the bus stop: 4, 5, 5, 6, 6, 6, 7, 7, 15. Describe the center, the spread and the shape. (Median 6 minutes. Range 15 - 4 = 11 minutes, although 8 of the 9 values lie between 4 and 7. Shape: a tight cluster with one outlier at 15.)
Differentiation Strategies
For Struggling Students
Give a sentence frame card: "A typical value is about ___ (center). The values go from ___ to ___ (spread). Most values are ___, and the shape is ___."
Have students cross off one value from each end of an ordered list, over and over, until one or two values are left, to find the median
Start every data set with a dot plot already drawn, so students can focus on describing it
For Advanced Students
Ask students to invent a data set of 10 values whose range is large even though 8 of the values are close together, and to explain why the range alone can mislead
Ask students to predict the shape of a real data set before collecting it, such as the number of siblings of each classmate, then collect it and compare
Ask why the median of two clusters can be a value that nobody has, and what they would report instead
Assessment Guidance
What to Look For
Check that students talk about all three features, not only a single number. For center, students should order the values before finding the middle one, and average the two middle values when the count is even. For spread, look for the range with units and for words that say whether most values are close together. For shape, students should use the vocabulary (peak, symmetric, skewed, tail, cluster, gap, outlier) and point to the part of the dot plot that shows it. A strong answer ties the description to the context, for example "most students sleep 8 to 9.5 hours".
02
Classroom Activities
3 Activities
1
Hand Span Dot Plot
20 minWhole class, then pairs
The class answers the statistical question "How long are the hand spans of students in our class?" Each student measures a hand span (the distance from the tip of the thumb to the tip of the little finger, with the hand stretched wide) and adds a dot to a class dot plot. Pairs then describe the distribution's center, spread and shape.
Procedure
Put a strip of masking tape on the board and mark it from 13 to 24 centimeters in half centimeters
Partners help each other measure the hand span of the writing hand to the nearest half centimeter with a centimeter ruler
Each student puts one dot sticker above his or her value, stacking dots that repeat
Pairs copy the dot plot and write one sentence each for center (the median), spread (the range, and where most values are) and shape
Sample Class Results (invented, 24 students)
15.5, 16, 16.5, 16.5, 17, 17, 17, 17.5, 17.5, 17.5, 18, 18, 18, 18, 18, 18.5, 18.5, 19, 19, 19.5, 20, 20, 21, 22.5 centimeters. Use these to preview the discussion, or with a class that works remotely.
Discussion Questions
In the sample results, what is the median hand span? (Halfway between the 12th and 13th values, both 18, so 18 centimeters)
What is the range of the sample results? (22.5 - 15.5 = 7 centimeters)
Where is the peak? (At 18 centimeters, with 5 dots, the most of any value)
Is there any value you would call an outlier? Why or why not? (22.5 stands a little apart, but the gap is only 1.5 centimeters, so many students will call the shape roughly symmetric with no clear outlier)
Would a class of adults have the same center? What would change?
Modification for Distance Learning
Students measure at home and type their value into a shared slide with a number line. The teacher drags one dot per value onto the line, and pairs describe the result in a breakout room.
2
Shape Card Sort
20 minGroups of 3-4
Each group gets 8 cards. Each card has an invented data set with its context. Groups make a quick dot plot of each card on grid paper, sort the cards into four shape groups (symmetric, skewed right, skewed left, two clusters) and write the median and the range on each card.
Shape Cards (8 cards, all data invented)
Card 1: times late to class this semester for 12 students: 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 5, 8
Card 2: percent correct on an easy spelling test for 12 students: 55, 70, 80, 85, 90, 90, 95, 95, 95, 100, 100, 100
Card 3: weights of 12 apples, in grams: 150, 158, 162, 165, 168, 170, 171, 174, 177, 180, 184, 191
Card 4: heights, in inches, of 12 people on a kindergarten field trip (children and adult helpers): 42, 43, 44, 45, 46, 47, 62, 64, 66, 67, 69, 71
Card 5: dollars spent at the school store in one day by 12 students: 1, 1, 2, 2, 2, 3, 3, 4, 5, 7, 10, 16
Card 6: days out of 20 that 12 students brought a water bottle: 4, 9, 12, 15, 16, 17, 18, 18, 19, 19, 20, 20
Card 7: raisins in 12 small boxes: 27, 29, 30, 30, 31, 31, 32, 32, 33, 34, 35, 37
Card 8: minutes spent in the library by 12 visitors: 3, 4, 5, 5, 6, 8, 45, 50, 55, 60, 60, 75
Answer Key
Skewed right: Cards 1 and 5. Skewed left: Cards 2 and 6. Roughly symmetric: Cards 3 and 7. Two clusters: Cards 4 and 8. Each group has exactly two cards.
Discussion Questions
Card 4 and Card 8 each have a gap. What is happening in real life that makes two groups? (Children and adults; people returning a book and people staying to study)
On Card 5, the range is 15 dollars. Does that mean most students spent a lot? (No: 7 of the 12 students spent 3 dollars or less; one 16-dollar purchase makes the range large)
Why might an easy test give a shape that is skewed left?
Variation: Make Your Own Card
Each group writes a ninth card with a real context from school life and a data set of 10 values, and another group sorts it.
3
Design a Distribution
15 minPairs
Pairs get three challenge cards. Each card describes a distribution of 10 game scores from 0 to 15 points by its center, spread and shape. Each pair writes a data set that fits and draws its dot plot, then trades with another pair, who checks all three features.
Challenge Cards (3 cards)
Challenge A: median 6, range 4, symmetric with one peak
Challenge B: median 3, range 9, skewed right
Challenge C: range 12, two clusters with a gap of at least 5 points between them
C: 2, 3, 3, 4, 4, 11, 12, 12, 13, 14 (range 14 - 2 = 12, gap from 4 to 11)
Discussion Questions
Did any two pairs write the same data set for Challenge A? What does that tell you about how much one center and one range tell you?
For Challenge C, where did your median land? Is it a good typical value?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Center, Spread and Shape on a Dot Plot
A dot plot of the invented sleep data from the first worked example, drawn to scale. The dashed line marks the center (the median, 9 hours). The bracket shows the spread from the smallest value, 6.5 hours, to the largest, 10.5 hours. The shape has one peak at 9 hours and is fairly symmetric.
Diagram 2: Skewed Left, Skewed Right and Two Clusters
Three invented data sets drawn to scale as dot plots. In the top plot, most scores are high and the tail stretches left toward 3 points (skewed left). In the middle plot, most students read few books and the tail stretches right toward 15 (skewed right). In the bottom plot, runners and walkers form two clusters, with a gap between 12 and 16 minutes.
04
Homework Assignment
~30 min
6.SP.A.2 Homework: Describing Distributions
Directions: All data sets are invented. For every data set, draw a dot plot and describe the center, the spread and the shape. Use the words from class (median, range, peak, symmetric, skewed, tail, cluster, gap, outlier) and include units.
Part 1: Describe One Distribution (Problems 1-2)
Fifteen students recorded the minutes they spent practicing a musical instrument yesterday: 5, 10, 15, 15, 20, 20, 20, 25, 25, 25, 30, 30, 35, 40, 60. Draw a dot plot. Find the median and the range. Describe the shape, and say whether any value looks like an outlier.
A class garden has 12 tomato plants. Their heights, in centimeters, are 38, 41, 43, 44, 45, 46, 46, 47, 48, 50, 51, 54. Draw a dot plot. Find the median and the range, and describe the shape.
Part 2: Compare Two Distributions (Problems 3-4)
Maya's points in 8 basketball games: 11, 12, 13, 13, 14, 15, 15, 17. Jess's points in 8 games: 4, 7, 9, 12, 14, 16, 18, 21. Find the median and the range for each player. Compare their centers and their spreads. Which player's score is easier to predict for the next game? Explain.
Noon temperatures, in degrees Fahrenheit, for the same 7 days in two towns. Hillview: 60, 63, 64, 65, 67, 67, 69. Bayside: 76, 79, 81, 82, 82, 84, 85. Find the median and the range for each town. Write two sentences: one comparing the centers and one comparing the spreads.
Part 3: Shape and the Statistical Question (Problems 5-6)
Predict the shape of each distribution and explain your reasoning in one sentence: (a) the number of countries each student in your school has visited; (b) the number of the 180 school days that each student in your school attended this year; (c) the heights of all the sixth graders in a large school.
Ravi asked 16 classmates, "How many hours did you spend outdoors last Saturday?" The answers were 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 8, 10. (a) Explain why Ravi's question is a statistical question. (b) Find the median and the range. (c) Describe the shape. (d) Write a short paragraph that describes the distribution using its center, spread and shape.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Dot Plots
Every dot plot has a scaled number line, a label and one dot per value
One dot plot is missing values or is not to scale
Dot plots missing
Center and Spread
Medians and ranges are correct, with units
One median or range is wrong, or units are missing
Most medians and ranges are wrong or missing
Shape
Shapes are named with the class vocabulary and tied to the dot plot
Shapes are named but not explained
Shapes missing
Comparing and Explaining
Comparisons name both center and spread and connect to the context
Comparison names only one feature
No comparison
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. All data sets are invented. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
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
Which statement describes the center of a data set?
Answer: B
The center is one typical value near the middle of the data, so "a typical value is about 21" describes the center. Choice A gives the smallest and largest values, which describes the spread. Choice C describes the shape. Choice D describes a gap, which is also part of the shape.
Question 2 of 20 · Multiple Choice
Invented data: the number of pets owned by 9 students is 0, 0, 1, 1, 1, 2, 2, 3, 4. What is the median?
Answer: C
There are 9 values in order, so the median is the 5th value: 1 pet. Choice A counts the 9 values and takes the middle of 0 to 4 on the number line instead of the middle value. Choice B is the smallest value, and choice D is the largest value, which also equals the range, 4 - 0 = 4.
Question 3 of 20 · Multiple Choice
Invented data: the lengths, in centimeters, of 8 pencils in a pencil cup are 11, 13, 14, 15, 16, 17, 18, 19. What is the range?
Answer: A
The range is the largest value minus the smallest: 19 - 11 = 8 centimeters. Choice B is the median, (15 + 16) ÷ 2 = 15.5, which measures center, not spread. Choice C adds the smallest and largest values (11 + 19) instead of subtracting. Choice D is the largest value.
Question 4 of 20 · Multiple Choice
Invented data: the number of goals scored by a soccer team in 12 games is 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7. Which word best describes the shape?
Answer: D
Most games have 0 to 2 goals, and a thin tail stretches toward 6 and 7, so the shape is skewed right. Choice B names the direction backward: the long tail is on the right side, where the high values are. Choice A would need about the same number of dots on both sides of the peak. Choice C would need a gap with a second group of values.
Question 5 of 20 · Multiple Choice
A distribution is skewed left. Which description fits it?
Answer: A
In a skewed-left distribution, the long tail points left, toward the low values, so most values are high. Choice B describes skewed right; students who name the skew by where the peak is, instead of where the tail is, pick it. Choice C describes two clusters, and choice D describes a symmetric shape.
Question 6 of 20 · Multiple Choice
Invented data: two classes timed how long, in seconds, students could balance on one foot. Class A: 20, 22, 23, 25, 25, 26, 28, 29. Class B: 8, 14, 19, 24, 26, 31, 37, 44. Which statement is true?
Answer: B
Class A's median is (25 + 25) ÷ 2 = 25 seconds and Class B's is (24 + 26) ÷ 2 = 25 seconds, so the centers are equal. Class A's range is 29 - 20 = 9 seconds and Class B's is 44 - 8 = 36 seconds, so Class B is much more spread out. Choice A reverses the ranges. Choices C and D say the ranges are equal and the medians differ, which mixes up center and spread.
Question 7 of 20 · Multiple Choice
Invented data: the ages of the 14 people at a grandparent and grandchild cooking class are 7, 8, 8, 9, 10, 10, 11, 62, 65, 67, 68, 70, 72, 75. Which description of the shape fits best?
Answer: A
Seven children are between 7 and 11, seven grandparents are between 62 and 75, and no one is between 11 and 62: two clusters with a gap. Choice C comes from looking at the middle of the number line, 7 to 75, instead of at the dots; there is no one near 40. Choices B and D describe one pile of values with a tail, but this data set has two separate piles.
Question 8 of 20 · Multiple Choice
For the cooking class data in the previous question, the median is (11 + 62) ÷ 2 = 36.5 years. Why is the median a poor description of this distribution?
Answer: D
The median falls in the middle of the gap, and no person in the class is anywhere near 36.5 years old. A better description names both clusters: children about 7 to 11 and grandparents about 62 to 75. Choice A confuses the median with the number halfway between the smallest and largest ages, (7 + 75) ÷ 2 = 41, and 41 is not typical either. Choice B describes the range. Choice C is false: 36.5 is 38.5 years below 75.
Question 9 of 20 · Multiple Choice
Which question would give data with a distribution that has a center, a spread and a shape?
Answer: C
Only choice C is a statistical question: different students give different answers, so the answers form a distribution. Choices A, B and D each have one answer, so there is no variability to describe with a center, a spread or a shape.
Question 10 of 20 · Multiple Choice
Invented data: the number of seconds 11 students took to solve a puzzle is 31, 33, 34, 35, 35, 36, 37, 38, 38, 40, 72. Which value is an outlier?
Answer: B
An outlier is a value far from the rest of the data. The other ten values lie between 31 and 40, and 72 is 32 seconds above the next largest value. Choice C is the median, the 6th value, which is the center. Choices A and D are the ends of the main cluster, only a few seconds from their neighbors.
Question 11 of 20 · Multiple Choice
Which description gives the center, spread and shape of a distribution?
Answer: D
Only choice D names all three features: a center (median 8 hours), a spread (range 4 hours) and a shape (symmetric, one peak). Choice B leaves out the shape. Choice C gives the spread and the shape but no center. Choice A gives a typical value and one end of the data, but no shape.
Question 12 of 20 · Multiple Choice
Invented data: plant heights, in centimeters, in two gardens. Garden P: 12, 14, 15, 15, 16, 18. Garden Q: 21, 24, 25, 26, 26, 27. How do the two distributions compare?
Answer: C
Garden P's median is (15 + 15) ÷ 2 = 15 centimeters and Garden Q's is (25 + 26) ÷ 2 = 25.5 centimeters, so the centers are different. The ranges are 18 - 12 = 6 and 27 - 21 = 6 centimeters, so the spreads are the same. Choice A mixes up center and spread. Choices B and D each get one of the two comparisons wrong.
Question 13 of 20 · Multiple Choice
A dot plot shows a symmetric distribution with one peak at 14. Where is the median most likely to be?
Answer: B
In a symmetric distribution with one peak, the values balance on both sides of the peak, so the middle value is close to the peak at 14. Choices A and C put the center at one end, which happens only when students confuse the median with the smallest or largest value. Choice D describes a two-cluster shape, not a symmetric one with one peak.
Question 14 of 20 · Multiple Choice
Invented data: Team X's race times have a range of 3 minutes and Team Y's have a range of 11 minutes. What does this tell you?
Answer: A
The range measures spread, so a smaller range means Team X's times are closer together. The range says nothing about which team is faster (choice B), which is a question about center. It does not count runners (choice C). Choice D subtracts the ranges, 11 - 3 = 8, and treats the difference as a difference in centers.
Question 15 of 20 · Short Answer
Invented data: the number of minutes 10 students spent on homework last night is 15, 20, 20, 25, 30, 30, 30, 35, 40, 45. Find the median and the range, and describe the shape.
In order, the 5th and 6th values are both 30, so the median is 30 minutes. The range is 45 - 15 = 30 minutes. The shape is roughly symmetric with one peak at 30: there are 4 values below 30 and 3 values above 30, and the ends are about the same distance from the peak.
Question 16 of 20 · Short Answer
Invented data: the ages, in months, of 10 puppies at a dog adoption event: 2, 3, 3, 4, 4, 4, 5, 6, 9, 14. Describe the center, the spread and the shape of this distribution.
Center: the median is (4 + 4) ÷ 2 = 4 months. Spread: the range is 14 - 2 = 12 months, although 8 of the 10 puppies are 2 to 6 months old. Shape:skewed right, with a peak at 4 months and a tail toward 14 months; 14 could be called an outlier.
Question 17 of 20 · Short Answer
Write a data set of 8 values whose median is 10 and whose range is 6. Explain how you know it works.
Many answers work. One is 7, 8, 9, 10, 10, 11, 12, 13. In order, the 4th and 5th values are 10 and 10, so the median is (10 + 10) ÷ 2 = 10. The range is 13 - 7 = 6. Any answer is correct if the average of the 4th and 5th values is 10 and the largest value minus the smallest is 6.
Question 18 of 20 · Short Answer
Two data sets both have a median of 50. Set 1 has a range of 4 and Set 2 has a range of 40. Describe how their dot plots would look different.
The centers are the same, so both dot plots are centered near 50. Set 1's dots are packed closely together, all within 4 units, for example from 48 to 52. Set 2's dots are spread across a much wider part of the number line, 40 units from the smallest to the largest value, for example from 30 to 70. The center alone cannot show this difference; the spread does.
Question 19 of 20 · Short Answer
A school collects the number of minutes each student spends riding to school. Most students live close by, but a few live far away. Predict the shape of the distribution and explain.
The shape is likely skewed right. Most students have short rides, so most values are low and the peak is on the left. The few students who live far away have long rides, which make a thin tail stretching to the right.
Question 20 of 20 · Short Answer
Invented data: a grocery store weighed 10 bags of "1-pound" grapes, in ounces: 15, 16, 16, 17, 17, 17, 17, 18, 18, 19. Describe the distribution by its center, spread and shape. (1 pound = 16 ounces.)
Center: the median is (17 + 17) ÷ 2 = 17 ounces, a little more than 1 pound. Spread: the range is 19 - 15 = 4 ounces, so the bags are close to each other. Shape:one peak at 17 ounces and symmetric: 3 bags weigh less than 17 ounces, 3 weigh more, and there are no gaps or outliers.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.SP.A.2 mean?
6.SP.A.2 means students understand that the answers to a statistical question form a distribution, and that a distribution can be described by three features. The center is a typical value, the spread tells how much the values vary, and the shape is the picture the data makes on a plot, such as symmetric, skewed or clustered.
Is 6.SP.A.2 taught in grade 6 or grade 7?
It is a grade 6 standard in the Statistics and Probability domain. Grade 6 students describe single distributions and compare two informally. In grade 7, 7.SP.B.3 and 7.SP.B.4 ask students to compare two distributions more carefully, using measures of center and variability to make inferences.
What is a distribution in math?
A distribution is the pattern of values in a data set: which values occur and how often each one occurs. A dot plot shows it well, because every value gets a dot and repeated values stack up. You can see at a glance where the data pile up, how wide the data stretch and whether there are gaps.
What is the difference between center and spread?
Center tells where the data are, and spread tells how far apart they are. Two groups of students can both have a typical score of 80 (same center) while one group's scores are all between 76 and 84 and the other's run from 50 to 100 (different spreads).
What does skewed right mean?
Skewed right means the long tail of the distribution points to the right, toward the high values. Most values are low, and a few high values stretch out the right side. Many students name the skew by where the peak is, which gives the wrong direction; the tail names the skew.
Which measures of center and spread do sixth graders use for 6.SP.A.2?
Students usually start with the median for center and the range for spread, because both come straight from an ordered list or a dot plot. Other measures come with 6.SP.A.3 and 6.SP.B.5: the mean (the fair-share average), the interquartile range (the range of the middle half of the data) and the mean absolute deviation (the average distance of the values from the mean). For this standard, clear words matter as much as numbers.
What is an outlier?
An outlier is a value that is far away from the rest of the data, often separated by a gap on the dot plot. In grade 6, students decide this by looking at the plot and the context. A formal rule for outliers comes in later grades.
Why isn't one number enough to describe data?
One number cannot show how the data vary or what shape they have. A median of 16.5 minutes could come from a group whose times are all close to 16.5, or from runners near 10 minutes and walkers near 20 minutes. Center, spread and shape together describe what really happened.
What are common mistakes students make with this standard?
A common mistake is finding the median without putting the values in order first. Another is reading the middle of the number line, or the middle of the value labels in a frequency table (a table that lists each value and how many times it occurs), instead of the middle value. Students also often reverse the direction of skew and describe only the center, leaving out spread and shape.
How can parents help with 6.SP.A.2 at home?
Parents can collect small data sets together with their child, such as the minutes each family member spends on chores for a week or the prices of cereal at the store. Ask three questions about each set: What is a typical value? How different are the values? What would the dot plot look like?
07
Related Standards
6 standards
These standards connect to 6.SP.A.2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.SP.A.1Prerequisite
Recognize a statistical question as one that expects variability in the data
