6.SP.B.5Common CoreMathStatistics and ProbabilityGrade 6
6.SP.B.5: Summarizing Data Sets in Context
In plain English: 6.SP.B.5 is the Common Core grade 6 math standard that asks students to summarize a numerical data set in its context. Students report the number of observations, what was measured, how and in what units, give a center (median or mean) and a spread (interquartile range or mean absolute deviation), describe patterns and striking values, and choose measures that fit the shape of the data.
Summarize numerical data sets in relation to their context, such as by:
a.Reporting the number of observations.
b.Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c.Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d.Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Common Core State Standards for Mathematics · Domain: Statistics and Probability (SP) · Cluster: Summarize and describe distributions. Also written as 6.SP.5 · Official standard
Students learn to summarize a data set so that someone who never saw the list of numbers understands it. A good summary has four parts, matching parts a-d of the standard. It reports the number of observations (data values). It describes the attribute (the thing being measured, such as reaction distance), how it was measured and its units. It gives a measure of center (one number for a typical value: the median, the middle value, or the mean, the sum divided by the count) and a measure of variability (one number for how spread out the values are: the interquartile range, or IQR, or the mean absolute deviation, or MAD). And it describes the overall pattern and any striking deviations (values far from the rest), with a reason from the context when there is one.
Students then learn to choose. When the data are roughly symmetric (about the same on both sides of the center), the mean and MAD work well. When the data are skewed (stretched out to one side) or have a value far from the rest, the median and IQR describe a typical value better, because one extreme value pulls the mean. Every data set on this page is invented for teaching, with realistic values for the objects and people named.
Learning Objectives
By the end of this lesson, students will be able to:
Report the number of observations and describe the attribute, how it was measured and its units
Find the median and the mean of a data set in context
Find the interquartile range and the mean absolute deviation, and explain what each says about spread
Describe the overall pattern of a data set and any striking deviations, with reasons from the context
Choose measures of center and variability that fit the shape of the data and the question
Prior Knowledge Required
Students should already be comfortable with:
Making dot plots, histograms and box plots, and finding the five-number summary 6.SP.B.4
Knowing that a measure of center describes a typical value with one number and a measure of variation describes spread 6.SP.A.3
Understanding absolute value as the distance of a number from 0 6.NS.C.7
Put two small invented data sets on the board: the minutes 5 students in each of two book clubs read last night.
Warm-Up Prompt
"Club A: 20, 25, 30, 35, 40 minutes. Club B: 0, 10, 30, 50, 60 minutes. Both clubs read an average of 30 minutes. Are the two clubs alike? What would you tell a teacher about each club in one sentence?"
Give pairs two minutes, then collect sentences. Students usually notice that both clubs have the same center, 30 minutes, but Club B is much more spread out: its readers range from 0 to 60 minutes, while Club A stays from 20 to 40. Tell the class that one number for the center is not enough to describe data. Today they learn a full summary: how many values, what was measured and in what units, a center, a spread, and anything unusual.
Direct Instruction20-25 minutes
Part 1: Report the data (parts a and b). Start every summary by naming the number of observations, the attribute, how it was measured, and the units. "10 students; time balanced on one foot with eyes closed; measured with a stopwatch; in seconds." How the data were measured matters: a stopwatch gives more exact times than counting out loud, and a survey answer such as "about 30 minutes" may be rounded.
Part 2: Center (part c). The mean is the sum of the values divided by the number of values. It is the "fair share": if every student gave all their seconds to one pile and split it evenly, each would get the mean. The median is the middle value of the ordered list, or the number halfway between the two middle values. Work Example 1 (below) for both.
Part 3: Variability (part c). The interquartile range (IQR) is Q3 minus Q1, where Q1 and Q3 are the medians of the lower and upper halves (as in box plots, leave the median out of the halves when the count is odd). It is the width of the middle half of the data. The mean absolute deviation (MAD) is the average distance of the values from the mean. Find the mean, find each value's distance from it (always positive, like an absolute value), add the distances and divide by the number of values. Diagram 2 shows the distances for Example 1. A small MAD or IQR means the values stay close together; a large one means they are spread out, as in Example 2.
Part 4: Pattern, deviations and choice (parts c and d). Describe the shape: where the values cluster (bunch together), where the peak (the tallest part of the plot) is, any gaps (empty stretches of the number line), and whether the data are symmetric or skewed. Name any value far from the rest and look for a reason in the context. Then choose: for skewed data or data with a far-away value, report the median and IQR (Example 3 and Diagram 1). For roughly symmetric data, the mean and MAD work well, and the mean and median are close anyway. Use Example 4 to model a sentence about the pattern.
A full summary with all four measures
A class used a stopwatch to time how long 10 students could balance on one foot with their eyes closed, to the nearest second (invented data): 4, 6, 7, 8, 9, 10, 11, 12, 14, 19 seconds.
Equation: 10 observations, in seconds. Mean = 100 ÷ 10 = 10; median = (9 + 10) ÷ 2 = 9.5; Q1 = 7 and Q3 = 12, so IQR = 5; distances from the mean add to 32, so MAD = 32 ÷ 10 = 3.2 seconds
Same mean, different spread (MAD)
Two basketball players each played 5 games (invented data). Player A scored 10, 12, 14, 16, 18 points. Player B scored 4, 8, 14, 20, 24 points.
Equation: Both means are 70 ÷ 5 = 14 points. Player A: distances 4, 2, 0, 2, 4, so MAD = 12 ÷ 5 = 2.4 points. Player B: distances 10, 6, 0, 6, 10, so MAD = 32 ÷ 5 = 6.4 points. Player A is more consistent
Skewed data: choosing the median and IQR
Eleven students reported how many minutes it takes them to get to school (invented data): 5, 6, 8, 8, 10, 12, 12, 15, 18, 20, 51.
Equation: Median = 12 minutes; IQR = 18 - 8 = 10 minutes. The mean is 165 ÷ 11 = 15 minutes, which is more than 7 of the 11 times, because the 51-minute trip pulls it up. The median and IQR describe a typical trip better
Pattern and a striking deviation
A histogram shows the weights of 30 dogs at an animal shelter, weighed on a floor scale in pounds (invented data). Bins 20 pounds wide from 0 to 140 have heights 3, 7, 11, 6, 2, 0 and 1.
Equation: 3 + 7 + 11 + 6 + 2 + 0 + 1 = 30 observations. Overall pattern: 24 of the 30 dogs weigh from 20 up to 80 pounds, with a peak at 40 up to 60. Striking deviation: one dog weighs from 120 up to 140 pounds, far from the rest; in context, it may be a giant breed such as a mastiff
Guided Practice15 minutes
Pairs write a full four-part summary for one data set, one sentence per part, while the teacher checks each sentence before they move on.
Lengths of the 12 pencils in the class pencil cup, measured with a centimeter ruler to the nearest centimeter (invented data)
Pencil
1
2
3
4
5
6
7
8
9
10
11
12
Length (cm)
7
9
10
11
12
12
13
14
15
16
18
19
Model answers: (a) 12 observations. (b) The attribute is pencil length, measured with a centimeter ruler to the nearest centimeter, in centimeters. (c) The median is (12 + 13) ÷ 2 = 12.5 cm. Q1 = (10 + 11) ÷ 2 = 10.5 cm and Q3 = (15 + 16) ÷ 2 = 15.5 cm, so the IQR is 5 cm. The mean is 156 ÷ 12 = 13 cm. (d) The lengths spread fairly evenly from 7 to 19 cm with no value far from the rest. A new pencil is about 19 cm, so the shorter pencils have been sharpened many times. Because the data are close to symmetric, the mean and median are close (13 and 12.5). Watch for pairs who forget the units or who find the median before ordering.
Independent Practice10-15 minutes
Each student works alone. The minutes 8 students took to finish a logic puzzle, timed with the classroom clock (invented data): 6, 8, 9, 10, 10, 11, 12, 14. (1) Report the number of observations, the attribute, how it was measured and the units. (8 students; puzzle time; classroom clock; minutes.) (2) Find the mean. (80 ÷ 8 = 10 minutes.) (3) Find the MAD. (Distances 4, 2, 1, 0, 0, 1, 2, 4 add to 14, and 14 ÷ 8 = 1.75 minutes.) (4) Find the median and compare it with the mean. (10 minutes, the same as the mean, because the data are symmetric.) (5) Write one sentence that a parent could understand. (A typical student took about 10 minutes, and most times were within about 2 minutes of that.)
Closure5 minutes
Exit ticket: a student measured the heights of 5 pepper plants with a ruler, in inches (invented data): 3, 5, 6, 7, 9. Report the number of observations and the units, then find the mean and the MAD. (5 plants, in inches; mean = 30 ÷ 5 = 6 inches; distances 3, 1, 0, 1, 3 give MAD = 8 ÷ 5 = 1.6 inches.) Then ask: if one plant had been 30 inches tall, would you still report the mean? (No: the median and IQR would describe a typical plant better.)
Differentiation Strategies
For Struggling Students
Give a summary frame with four blanks: "There are ___ observations of ___, measured with ___ in ___. A typical value is ___ and the spread is ___. Most values ___, except ___."
Use a table with columns "value", "distance from the mean" for every MAD problem, so each step is written down
Start with data sets of 5 values and whole-number means before moving to larger sets
For Advanced Students
Ask students to build two data sets of 6 values with the same mean but a MAD of 1 and a MAD of 5
Give a data set and ask how the mean, median, IQR and MAD change if the largest value is doubled, then explain which measures change and why
Ask students to find a real data set they care about, such as their own sleep times for a week, and write a full four-part summary
Assessment Guidance
What to Look For
Check that every summary names the number of observations, the attribute and its units, and how the data were measured. In calculations, look for ordered data before finding a median, both halves used for the IQR, and distances (not signed differences) in the MAD. In the pattern sentence, students should name where values cluster and point to any value far from the rest with a reason from the context. When students choose measures, ask them to say why: the shape of the data and the question being asked should both appear in the reason.
02
Classroom Activities
3 Activities
1
Ruler Drop Reaction Test
20 minPairs, then groups of 4
Students measure their reaction distance with a falling ruler, pool the class data, and write a full four-part summary.
Procedure
One partner holds a 30 cm ruler at the 30 cm end so it hangs down, with the 0 mark level with the other partner's open thumb and finger
Without warning, the holder lets go. The catcher pinches the ruler as fast as possible, and the pair reads the mark at the top of the thumb to the nearest centimeter
Each student does one practice drop and one recorded drop, then writes the recorded distance on a sticky note
The class makes a dot plot of all the sticky notes. Groups of 4 copy the data and write the summary
Sample Class Data (invented, for teacher planning)
12 students, in centimeters: 13, 15, 16, 17, 18, 18, 19, 20, 21, 22, 24, 29. For these data the median is 18.5 cm and the IQR is 5 cm. The 29 cm catch is far from the rest; in context, that student may have looked away.
Discussion Questions
What is the attribute, and what are its units? Would the summary change if we measured to the nearest half centimeter?
Why do we allow a practice drop? How might it change the data?
Is there a catch far from the rest? What might explain it?
Should our class report the median and IQR or the mean and MAD? Look at the shape of the dot plot first
Modification for Distance Learning
Students use a free online reaction-time clicker instead of a ruler, record their time in milliseconds, and enter it in a shared spreadsheet that the class summarizes together.
2
Mean or Median? Scenario Card Sort
15 minGroups of 3
Each group gets 4 scenario cards with small invented data sets. Groups compute both measures of center for each card, then sort the cards into "mean and MAD fit" and "median and IQR fit".
Scenario Cards (4 cards)
Card 1, ages of the 8 people at a grade 6 birthday party, in years: 11, 11, 11, 12, 12, 12, 12, 41
Card 2, masses of the 6 eggs in a carton, weighed on a kitchen scale in grams: 56, 57, 58, 58, 59, 60
Card 3, text messages 7 students sent yesterday, from their own count: 0, 2, 3, 5, 6, 8, 60
Card 4, daily high temperatures for 5 days in May, from a weather website, in °F: 68, 70, 71, 72, 74
Procedure
For each card, one student finds the mean, one finds the median, and one sketches a quick dot plot
Compare the mean and median. If they are far apart, look at the dot plot for a value far from the rest
Sort the cards and write one reason on each card that uses both the shape and the context
Discussion Questions
On which cards are the mean and median far apart? (Cards 1 and 3)
On card 1, which value pulls the mean, and who might that person be?
For card 3, is the median or the mean a better answer to "how many texts does a typical student send?"
Challenge Variation
Groups change one value on card 2 so that the median and IQR become the better choice, and explain which value they changed and why.
3
Cube Towers: Fair Share and Distance
15 minPairs
Pairs use linking cubes to see the mean as a fair share and the MAD as the average number of cubes each tower is away from it.
Materials and Data
25 linking cubes per set, two sets per pair
Set A towers: 2, 4, 5, 7, 7 cubes
Set B towers: 1, 3, 5, 8, 8 cubes
Procedure
Build the 5 towers of Set A. Move cubes between towers until all towers are the same height. That height is the mean
Rebuild the original towers. For each tower, count how many cubes it is above or below the mean and write that distance on a sticky note
Add the 5 distances and divide by 5 to get the MAD. Repeat for Set B
Discussion Questions
Both sets level out to the same height. What is it? (5 cubes)
Which set has the larger MAD? (Set B: 2.4 cubes, compared with 1.6 for Set A)
Why do we count distances instead of "above" as plus and "below" as minus?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Skewed Data Pull the Mean
The 11 travel times from Example 3 as a dot plot (top) and a box plot (bottom) on the same scale. One 51-minute trip stretches the data to the right. It pulls the mean (red) to 15 minutes, while the median stays at 12. The box shows the IQR: the middle half of the times lies from 8 to 18 minutes.
Diagram 2: Mean Absolute Deviation as Distance
The 10 balance times from Example 1, one per row. Each blue bar is the distance from a time to the mean of 10 seconds (the dashed red line). Adding the distances and dividing by 10 gives the mean absolute deviation, 3.2 seconds: on average, a time is 3.2 seconds from the mean.
04
Homework Assignment
~30 min
6.SP.B.5 Homework: Summarizing Data in Context
Directions: Show every step. Write the units with every measure. When you choose a measure, give a reason that uses the shape of the data and the context.
Part 1: Reporting the Data (Problems 1-2)
A science club measured the length of leaves from one maple tree with a ruler, to the nearest half centimeter (invented data): 8, 8.5, 9, 9.5, 10, 10, 10.5, 11, 11, 11.5, 12, 12.5, 13, 16. (a) How many observations are there? (b) Name the attribute, how it was measured and its units. (c) Find the median.
A class survey asked, "How many minutes did you practice a musical instrument yesterday?" A dot plot of the answers (invented data) has 4 dots at 0, 3 dots at 15, 5 dots at 20, 6 dots at 30, 2 dots at 45 and 1 dot at 120. (a) How many students answered? (b) What are the units, and why might a survey give less exact data than a timer? (c) Describe the overall pattern and any striking deviation, and give a possible reason for it.
Part 2: Center and Variability (Problems 3-4)
Five friends counted how many sit-ups each could do in 1 minute (invented data): 22, 25, 28, 30, 35. Find the mean and the mean absolute deviation. Write one sentence that explains what the MAD tells you.
The prices, in dollars, of 10 video games in a sale bin (invented data): 7, 9, 11, 11, 13, 15, 16, 19, 22, 25. Find the median, Q1, Q3 and the interquartile range. Explain what the IQR tells a shopper.
Part 3: Choosing Measures (Problems 5-6)
Nine students reported their weekly allowance in dollars (invented data): 0, 4, 6, 7, 9, 10, 11, 16, 72. Find the mean and the median. Which one better describes a typical allowance in this group? Which measure of variability goes with it? Explain using the shape of the data.
Two runners timed five 400-meter races each, in seconds (invented data). Runner A: 78, 79, 80, 81, 82. Runner B: 72, 76, 80, 84, 88. Find the mean and the MAD for each runner. The coach needs a runner with a predictable time for a relay. Whom should she pick? Explain with your numbers.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Reporting
Number of observations, attribute, method and units all correct
One of the four parts missing or wrong
Two or more parts missing
Calculations
Mean, median, IQR and MAD correct with units
One calculation error or missing units
Several errors or missing work
Pattern and Deviations
Clusters and striking values described with a reason from the context
Pattern described with no reference to the context
No description
Choosing Measures
Choice matches the shape of the data and is explained
Correct choice with a weak reason
Choice missing or does not fit the data
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. All data sets in the quiz are 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
A dot plot of shoe sizes in a class has stacks of 2, 5, 7, 4 and 2 dots. How many observations are there?
Answer: C
Each dot is one observation: 2 + 5 + 7 + 4 + 2 = 20. Choice A counts the stacks, which is the number of different shoe sizes. Choice B is the height of the tallest stack. Choice D leaves out one of the two stacks of 2.
Question 2 of 20 · Multiple Choice
Maya timed how long each of 15 classmates took to solve a puzzle cube. Which statement describes how the data were measured?
Answer: A
How the data were measured means the tool and the units, here a stopwatch and seconds. Choice B reports the number of observations. Choice C is a measure of center. Choice D describes the spread. All are parts of a summary, but only A answers the question.
Question 3 of 20 · Multiple Choice
Students weighed apples from a school garden on a kitchen scale. Which unit makes sense for these data?
Answer: B
A scale measures mass, so grams fit. Choice A is a unit of length, which a ruler would measure. Choice C is a unit of volume for liquids. Choice D is a unit for temperature or angles.
Question 4 of 20 · Multiple Choice
Leo read 12, 18, 20, 25 and 30 pages on five days. What is the mean number of pages per day?
Answer: D
The sum is 12 + 18 + 20 + 25 + 30 = 105 pages, and 105 ÷ 5 = 21 pages. Choice A is the median, the middle value. Choice B divides by 4 instead of 5. Choice C is the sum, before dividing.
Question 5 of 20 · Multiple Choice
Eight students counted the books in their backpacks (invented data): 5, 11, 2, 8, 13, 4, 9, 6. What is the median?
Answer: A
In order: 2, 4, 5, 6, 8, 9, 11, 13. The two middle values are 6 and 8, so the median is (6 + 8) ÷ 2 = 7. Choice B averages the two middle numbers of the unordered list, 8 and 13. Choice C is the mean, 58 ÷ 8. Choice D uses only one of the two middle values.
Question 6 of 20 · Multiple Choice
Twelve students answered questions in a 20-question trivia game (invented data): 2, 4, 5, 5, 6, 8, 9, 10, 11, 13, 14, 18 correct answers. What is the interquartile range?
Answer: B
The lower half 2, 4, 5, 5, 6, 8 gives Q1 = (5 + 5) ÷ 2 = 5, and the upper half 9, 10, 11, 13, 14, 18 gives Q3 = (11 + 13) ÷ 2 = 12. IQR = 12 - 5 = 7. Choice A is the range, 18 - 2. Choice C is the median, (8 + 9) ÷ 2. Choice D is Q3 alone, without subtracting Q1.
Question 7 of 20 · Multiple Choice
Four tomato seedlings are 6, 8, 12 and 14 cm tall (invented data). Their mean is 10 cm. What is the mean absolute deviation?
Answer: D
The distances from 10 are 4, 2, 2 and 4. They add to 12, and 12 ÷ 4 = 3 cm. Choice A adds the signed differences (-4, -2, 2, 4), which always cancel to 0. Choice B adds the distances but forgets to divide by 4. Choice C is the range, 14 - 6.
Question 8 of 20 · Multiple Choice
Fifteen students timed how long it takes them to get ready for school. Most took 20 to 40 minutes, but one took 120 minutes. Which measures should summarize these data?
Answer: B
One value far from the rest pulls the mean and the MAD, so the median and IQR describe the typical time and spread better. Choice A uses every value, which is the problem here: the 120 minutes pulls the mean up. Choices C and D mix one measure that the far value pulls with one that it does not, so the pair does not match.
Question 9 of 20 · Multiple Choice
The number of students who visited the school library on 10 days (invented data) was 45, 48, 50, 47, 46, 3, 49, 51, 44, 48. Which statement best describes a striking deviation?
Answer: A
Nine days fall from 44 to 51, and one day had 3 visitors, far below the rest. A good description names the value and looks for a reason in the context. Choice B ignores the big gap between 3 and 44. Choice C treats the median as if it described every value. Choice D picks the largest value, but 51 is only 1 more than the next value, 50.
Question 10 of 20 · Multiple Choice
On a science test, Class A has a mean absolute deviation of 3 points and Class B has a MAD of 9 points. What does this tell you?
Answer: C
The MAD is the average distance from the mean, so a larger MAD means the scores are more spread out. Choice A confuses spread with center: the MAD says nothing about which class scored higher. Choice B confuses spread with the number of observations. Choice D treats an average distance as an exact gap between all scores.
Question 11 of 20 · Multiple Choice
Five quiz scores are 70, 82, 85, 88 and 90. The 70 is a typing mistake and is changed to 20. What happens to the mean and the median?
Answer: A
The sum drops by 50, from 415 to 365, so the mean drops from 83 to 73. The middle value is still 85, so the median does not change. Choice B forgets that the median depends only on the middle value. Choice C reverses the two measures. Choice D forgets that the mean uses every value.
Question 12 of 20 · Multiple Choice
A class measured 9 bean plants after 3 weeks with a centimeter ruler. The median was 14 cm and the IQR was 3 cm. Which sentence summarizes the data best?
Answer: A
A good summary gives the measures with their units and the context: 9 plants, heights in centimeters. Choice B leaves out the context and the units. Choice C misreads the IQR: it describes only the middle half of the data, not every plant. Choice D claims too much, because the data come from only 9 plants in one class.
Question 13 of 20 · Multiple Choice
A dot plot of data is roughly symmetric, with no values far from the rest. Which statement about the center is true?
Answer: C
In symmetric data the mean and median are close, so either describes a typical value, and the mean and MAD are a good pair. Choice A is false: these data have no extreme values. Choice B is too strong: the median is also fine here. Choice D is false: symmetric data have a clear center.
Question 14 of 20 · Multiple Choice
Half of a class measured their arm spans in inches and the other half in centimeters. The teacher put all 24 numbers into one list and found the mean. What is the problem?
Answer: D
A summary must use one unit. Mixing inches and centimeters makes the numbers impossible to compare, so any center or spread found from them is meaningless. Choice A is wrong because 24 observations are enough. Choice B does not fix the problem: the median of mixed units is meaningless too. Choice C is wrong: arm span is measured with a tape measure.
Question 15 of 20 · Short Answer
Five students waited these numbers of minutes for a bus (invented data): 3, 5, 6, 9, 12. Find the mean and the mean absolute deviation, with units.
Sum: 3 + 5 + 6 + 9 + 12 = 35, so the mean is 35 ÷ 5 = 7 minutes. Distances from 7: 4, 2, 1, 2, 5, which add to 14. MAD = 14 ÷ 5 = 2.8 minutes: on average, a wait is 2.8 minutes away from the mean. A common error is to add the signed differences, which gives 0.
Question 16 of 20 · Short Answer
The ages of 11 singers in a youth choir are (invented data): 8, 9, 9, 10, 11, 11, 13, 14, 14, 16, 18 years. Find the median, Q1, Q3 and the interquartile range.
The data are in order. The median is the 6th value, 11 years. The lower half 8, 9, 9, 10, 11 gives Q1 = 9, and the upper half 13, 14, 14, 16, 18 gives Q3 = 14. IQR = 14 - 9 = 5 years: the middle half of the singers are within 5 years of age of each other.
Question 17 of 20 · Short Answer
A school nurse used a digital ear thermometer to record the body temperature of 18 students, to the nearest tenth of a degree Fahrenheit. Write the first two parts of a summary: the number of observations, and the attribute with how it was measured and its units.
18 observations. The attribute is body temperature, measured with a digital ear thermometer to the nearest tenth of a degree, in degrees Fahrenheit (°F). The method matters: an ear thermometer can read a little differently from a mouth thermometer, so the summary should say which one was used.
Question 18 of 20 · Short Answer
Eight phone calls lasted these numbers of minutes (invented data): 2, 3, 3, 4, 5, 5, 6, 44. Find the mean and the median. Which one better describes a typical call? Explain.
Mean: 72 ÷ 8 = 9 minutes. Median: (4 + 5) ÷ 2 = 4.5 minutes. The median describes a typical call better. The 44-minute call is far from the rest and pulls the mean up, so the mean is longer than 7 of the 8 calls. The IQR would be the matching measure of spread.
Question 19 of 20 · Short Answer
A park counted its visitors each day for two weeks, starting on a Monday (invented data): 120, 135, 128, 140, 131, 310, 305, 125, 138, 129, 133, 142, 298, 315. Describe the overall pattern and explain it with the context.
The data form two clusters. The 10 weekday counts fall from 120 to 142, and the 4 counts from 298 to 315 all fall on Saturdays and Sundays. In context, more people visit a park on weekends. A single mean of all 14 days would describe neither a typical weekday nor a typical weekend day, so it is better to summarize the two groups separately.
Question 20 of 20 · Short Answer
Two pizza shops each delivered 5 orders, and the delivery times in minutes were (invented data): Shop A: 28, 30, 30, 31, 31; Shop B: 15, 22, 30, 38, 45. Find the mean and MAD for each shop. Which shop would you call if you need the food at a predictable time?
Both means are 30 minutes (150 ÷ 5). Shop A: distances 2, 0, 0, 1, 1, so MAD = 4 ÷ 5 = 0.8 minutes. Shop B: distances 15, 8, 0, 8, 15, so MAD = 46 ÷ 5 = 9.2 minutes. Call Shop A: its times stay within about a minute of 30, while Shop B can be 15 minutes early or late.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.SP.B.5 mean?
6.SP.B.5 means students can summarize a numerical data set in its real context. A full summary reports how many observations there are, what was measured, how and in what units, a measure of center and a measure of spread, and the overall pattern with any values far from the rest. Students also choose measures that fit the shape of the data.
Is 6.SP.B.5 taught in grade 6 or grade 7?
It is a grade 6 standard, and it usually comes right after students learn dot plots, histograms and box plots (6.SP.B.4). In grade 7, students use the same measures to compare two groups (7.SP.B.3 and 7.SP.B.4), and in high school they add the standard deviation (HSS.ID.A.2).
How do you find the mean absolute deviation?
Find the mean, then find how far each value is from the mean, counting every distance as positive. Add the distances and divide by the number of values. For 2, 6, 7 and 9, the mean is 6, the distances are 4, 0, 1 and 3, and the MAD is 8 ÷ 4 = 2.
What is the difference between the IQR and the range?
The range is the maximum minus the minimum, so it depends on the two most extreme values. The IQR is Q3 minus Q1, the width of the middle half of the data, so a single far-away value does not change it much. That is why the IQR is part of this standard and the range is not.
When should students use the median instead of the mean?
Use the median, with the IQR, when the data are skewed or have a value far from the rest, such as incomes or travel times with one long trip. Use the mean, with the MAD, when the data are roughly symmetric. When in doubt, find both centers: if they are far apart, the median is usually the safer description of a typical value.
Why does 6.SP.B.5 ask for the number of observations and the units?
Because the same numbers can mean very different things. A mean of 12 is useless until you know it is 12 minutes for 11 students, or 12 pounds for 300 dogs. The number of observations also tells a reader how much to trust the summary: 5 values say less than 500.
What counts as a striking deviation?
A striking deviation is a value, or a group of values, far from the overall pattern, such as one test score of 35 when the other scores are from 80 to 95. In grade 6, students decide this by looking at a plot and the context. A formal rule for outliers comes later, in high school statistics (beyond this standard).
What are common mistakes on 6.SP.B.5 problems?
Common mistakes are finding the median before putting the data in order, adding signed differences for the MAD so they cancel to 0, forgetting units, and reporting the mean for data with a far-away value. Another is describing a pattern without the context, such as "the data go up" instead of "weekend visits are higher".
How is 6.SP.B.5 tested?
Test questions often give a small data set or a plot in a real context and ask for a mean, median, IQR or MAD. Others ask which measure fits a given data set best, or ask students to write a short summary. Students should show the ordered list and each distance, so a teacher can see where an error happened.
How can parents help with data summaries at home?
Pick something the family can measure for a week, such as minutes of sleep or the price of gas. Ask your child how many values there are, what the units are, what a typical value is and how spread out the values are. Then ask whether any day stands out and why.
07
Related Standards
6 standards
These standards connect to 6.SP.B.5: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.SP.A.3Prerequisite
Know that a measure of center summarizes data with one number and variation with another
