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Statistical questions
Recognize questions that expect variability in their answers.
Worked examples + 20 practice questions
Grade 6 Statistics and Data Review
Learn how to ask statistical questions, display numerical data, calculate center and spread, and describe distributions clearly.
This guide follows the major Grade 6 statistics expectations for variability, data displays, center, spread, and distribution summaries. View the official mathematics standards. State and district sequences may differ.
Statistics map
Six connected Grade 6 statistics skills
Statistics is not only calculation. Students must connect the numbers to the original question and context.
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Variability
Describe how values differ and why variation matters.
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Data displays
Read and create dot plots, histograms, and box plots.
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Center
Calculate and interpret mean and median.
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Spread
Calculate range, IQR, and mean absolute deviation.
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Distribution summaries
Describe shape, clusters, gaps, peaks, and possible outliers.
Concept 1
A statistical question expects different answers
The question must involve a group or repeated measurements where variability is possible.
Not statistical
- How old is Maya?
- What is the temperature at noon today?
- How many pages are in this book?
Each question asks for one specific value.
Statistical
- How old are the students in Grade 6?
- What are the noon temperatures during July?
- How many pages are in the books students read this month?
Each question expects a collection of varying values.
Quick test: Would collecting the answers produce a data set with possible variation? If yes, the question is statistical.
Concept 2
Choose a data display that matches the purpose
Each display emphasizes different features of a numerical data set.
Dot plot
Best for a small data set when individual values and frequencies matter.
123456
The tallest stack shows the most frequent value.
Histogram
Best for showing how many values fall inside numerical intervals.
Histogram bars touch because the intervals form a continuous numerical scale.
Box plot
Best for summarizing the five-number summary and comparing spread.
MinQ1MedianQ3Max
The box contains the middle 50% of the data.
Concept 3
Measures of center and spread answer different questions
Center describes a typical location. Spread describes how far the values vary.
Mean
Sum of values ÷ number of values
Balances the data as if the total were shared equally.
Median
Middle ordered value
Resists the effect of a very high or very low value.
Range
Maximum − minimum
Uses only the two extreme values.
Interquartile range
Q3 − Q1
Measures the spread of the middle half of the data.
Mean absolute deviation
Average distance from the mean
Describes typical distance from the mean.
Five-number summary
Minimum, Q1, median, Q3, maximum
Provides the values used to construct a box plot.
Choosing mean or median
- Use the mean when the distribution is reasonably balanced and every value should influence the center.
- Use the median when the data are skewed or contain an extreme value that would pull the mean.
- Match mean with MAD when describing center and spread together.
- Match median with IQR when describing a skewed distribution or one with outliers.
Step by step
Eight worked statistics examples
Order the data first whenever median, quartiles, or range are required.
1. Identify a statistical question
Which question is statistical: “How tall is Carlos?” or “How tall are the students in Carlos's class?”
- The first asks for one fixed value.
- The second expects several values with variation.
Answer: How tall are the students in Carlos's class?
2. Find the mean
Find the mean of 4, 6, 7, 8, and 10.
- Add: 4 + 6 + 7 + 8 + 10 = 35.
- There are 5 values.
- 35 ÷ 5 = 7.
Answer: 7
3. Find the median
Find the median of 12, 5, 9, 3, and 8.
- Order the data: 3, 5, 8, 9, 12.
- The middle value is 8.
Answer: 8
4. Find the range
Find the range of 14, 18, 21, 25, and 31.
- Maximum = 31.
- Minimum = 14.
- 31 − 14 = 17.
Answer: 17
5. Find the IQR
Find the IQR of 2, 4, 5, 7, 9, 10, 13, and 16.
- Lower half: 2, 4, 5, 7, so Q1 = 4.5.
- Upper half: 9, 10, 13, 16, so Q3 = 11.5.
- IQR = 11.5 − 4.5 = 7.
Answer: 7
6. Find the MAD
Find the MAD of 2, 4, 6, 8, and 10.
- Mean = 6.
- Distances from 6: 4, 2, 0, 2, 4.
- Average distance = 12 ÷ 5 = 2.4.
Answer: 2.4
7. Choose mean or median
The data are 12, 13, 13, 14, 15, and 42. Which center better represents a typical value?
- The value 42 is much larger than the others.
- It pulls the mean upward.
- The median is less affected.
Answer: Median
8. Describe a distribution
A dot plot has most values between 6 and 10, a peak at 8, a gap from 11 to 14, and one value at 15.
- Identify the cluster: 6 to 10.
- Identify the peak: 8.
- Identify the gap: 11 to 14.
- The value 15 may be an outlier depending on the full data.
Answer: Cluster at 6–10, peak at 8, gap at 11–14, possible high outlier at 15
Concept 4
Describe a distribution completely
A strong summary connects numerical features to the original context.
Context
What was measured, in what units, and for which group?
Number of observations
How many values are in the data set?
Center
What value represents a typical location?
Spread
How much do the values vary?
Shape
Is the distribution symmetric, skewed, clustered, or irregular?
Unusual features
Are there peaks, gaps, or possible outliers?
Model distribution summary
The data show the number of minutes 20 students spent reading. The distribution is slightly right-skewed, with a median of 24 minutes and an IQR of 10 minutes. Most values fall between 18 and 30 minutes, with one unusually high value near 50 minutes.
Error prevention
Common Grade 6 statistics mistakes
Not ordering the data
Median, quartiles, and range should be found from an ordered data set.
Dividing by the wrong count
For the mean, divide the total by the number of data values.
Confusing range and IQR
Range uses maximum and minimum; IQR uses Q3 and Q1.
Treating histogram bars as categories
Histogram intervals represent continuous numerical ranges.
Choosing mean automatically
Extreme values can make the median more representative.
Reporting numbers without context
A complete summary should state what the values and units represent.
Independent practice
20 Grade 6 statistics and data questions
Order data where necessary and explain choices of center or display.
A. Statistical questions and data displays
- Which is statistical: “How many pets does Jonah have?” or “How many pets do students in Grade 6 have?”
- Explain why “What are the daily high temperatures this week?” is statistical.
- Which display is best for showing every value in a small numerical data set: dot plot, histogram, or box plot?
- Which display is best for showing frequencies within intervals?
- Which display directly shows the five-number summary?
B. Mean, median, and range
- Find the mean of 6, 8, 9, 12, and 15.
- Find the median of 11, 4, 9, 7, and 13.
- Find the median of 3, 5, 6, 8, 12, and 14.
- Find the range of 18, 22, 25, 31, and 37.
- The mean of five numbers is 12. What is their total?
C. Quartiles, IQR, and MAD
- Find Q1 and Q3 for 2, 4, 6, 8, 10, 12, 14, and 16.
- Find the IQR for 1, 3, 5, 7, 9, 11, 13, and 15.
- Find the MAD of 3, 5, 7, 9, and 11.
- A data set has Q1 = 14 and Q3 = 26. Find the IQR.
- Which measure of spread is usually paired with the median: range, IQR, or MAD?
D. Interpretation and comparison
- The data are 8, 9, 10, 10, 11, and 40. Is mean or median more representative? Explain.
- A distribution has a cluster from 12 to 18 and no values from 19 to 25. What feature occurs from 19 to 25?
- Data set A has mean 20 and MAD 2. Data set B has mean 20 and MAD 7. Which set is more spread out?
- A box plot has minimum 4, Q1 7, median 10, Q3 15, and maximum 19. Find the range and IQR.
- Write one sentence summarizing a data set with median 25, IQR 8, and one unusually high value.
Complete all four sections before opening the answer key.
Go to the Answer KeyCheck your work
Statistics answer key
Use the explanation to identify whether the error involved calculation, display choice, or interpretation.
Question 1How many pets do students in Grade 6 have?
It expects a collection of varying answers.
Question 2The temperature can differ from day to day.
Repeated measurements produce a data set with variability.
Question 3Dot plot
A dot plot preserves each individual value.
Question 4Histogram
A histogram groups numerical values into intervals.
Question 5Box plot
It represents minimum, Q1, median, Q3, and maximum.
Question 610
The sum is 50 and 50 ÷ 5 = 10.
Question 79
Ordered data: 4, 7, 9, 11, 13.
Question 87
Average the two middle values: (6 + 8) ÷ 2 = 7.
Question 919
37 − 18 = 19.
Question 1060
Total = mean × number of values = 12 × 5.
Question 11Q1 = 5 and Q3 = 13
Lower half median is 5; upper half median is 13.
Question 128
Q1 = 4 and Q3 = 12, so 12 − 4 = 8.
Question 132.4
Mean is 7; distances are 4, 2, 0, 2, and 4; average distance is 12 ÷ 5.
Question 1412
26 − 14 = 12.
Question 15IQR
Median and IQR are commonly reported together.
Question 16Median
The value 40 pulls the mean upward and is far from the other values.
Question 17A gap
No values occur in that interval.
Question 18Data set B
Its larger MAD indicates greater typical distance from the mean.
Question 19Range = 15; IQR = 8
19 − 4 = 15 and 15 − 7 = 8.
Question 20Example: The data have a median of 25 and an IQR of 8, with one unusually high value.
A valid answer states center, spread, and the unusual feature.
Choose the next review from the error pattern
- Questions 1–5: review statistical questions and data-display purposes.
- Questions 6–10: review mean, median, range, and totals.
- Questions 11–15: review quartiles, IQR, and MAD.
- Questions 16–20: review interpretation, spread comparison, and distribution summaries.
Focused review
A five-session Grade 6 statistics plan
Questions and variability
Identify statistical questions and explain expected variation.
Data displays
Read and create dot plots, histograms, and box plots.
Center
Calculate and interpret mean and median.
Spread
Calculate range, IQR, and MAD.
Distribution summaries
Describe context, center, spread, shape, and unusual features.
Frequently asked questions
Grade 6 statistics and data FAQ
What statistics skills are taught in Grade 6?
Grade 6 students learn to recognize statistical questions, understand variability, display numerical data using dot plots, histograms, and box plots, and summarize distributions using measures of center and spread.
What is the difference between mean and median?
The mean is the total of all values divided by the number of values. The median is the middle value after the data are ordered. The mean is more affected by extreme values.
What is interquartile range?
The interquartile range, or IQR, is the difference between the third quartile and first quartile. It describes the spread of the middle half of the data.
What is mean absolute deviation?
Mean absolute deviation, or MAD, is the average distance of the data values from the mean. A larger MAD indicates greater spread around the mean.
How should a student describe a distribution?
A complete description may include the context, number of observations, center, spread, overall shape, clusters, gaps, peaks, and possible outliers.
Which data display should a Grade 6 student use?
Use a dot plot for a small data set where individual values matter, a histogram for grouped numerical intervals, and a box plot for comparing center and spread efficiently.
Standards reference and scope
This guide is organized around the Grade 6 Statistics and Probability standards covering statistical variability, numerical data displays, measures of center and spread, and distribution summaries. Read the official Common Core mathematics standards. GradeCove is an independent educational publisher and is not endorsed by the Common Core State Standards Initiative.
Need complete Grade 6 revision?
Use the full revision pack for structured practice across ratios, number systems, algebra, geometry, and statistics.