Grade 6 · Grade 6: Data and Distributions · Describing Data
Statistical Questions and Distributions
Ask questions that expect variability, display data three ways and describe centre, spread and shape.
Learning objectives
- Recognise a statistical question.
- Display data in dot plots, histograms and box plots.
- Calculate mean, median, mode and range.
- Describe spread using interquartile range and mean absolute deviation.
AERO Mathematics alignment
AERO.M6.SP.1
Recognise a statistical question as one that anticipates variability in the data related to the question.
AERO.M6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution described by its centre, spread and overall shape.
AERO.M6.SP.3
Recognise that measures of centre summarise data with a single number, while measures of variation describe how values differ.
AERO.M6.SP.4
Display numerical data in plots on a number line, including dot plots, histograms and box plots.
AERO.M6.SP.5
Summarise numerical data sets by describing measures of centre and variability, including interquartile range and mean absolute deviation.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion B — Investigating patterns
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
Two questions: How tall am I? and How tall are the students in Grade 6?
Think about it
Only one of these is a statistical question. Which one, and why?
Hint: Statistics begins where answers vary.
EXPLAIN
Describing a distribution
A statistical question anticipates variability. The answers form a distribution, which we describe using centre, spread and shape.
| Measure | What it tells you | Watch out for |
|---|---|---|
| Mean | The balance point of the data | Pulled strongly by outliers |
| Median | The middle value in order | More reliable with outliers |
| Mode | The most frequent value | May not exist or may be several |
| Range | Maximum minus minimum | Uses only two values |
| IQR | Spread of the middle 50% | Resistant to outliers |
| MAD | Average distance from the mean | Good for comparing consistency |
Choosing a display
- Dot plot: small data sets, shows every value.
- Histogram: larger data sets grouped into intervals, shows shape.
- Box plot: shows median, quartiles and outliers, ideal for comparing groups.
Common misconception
The mean is not always the typical value. In a class where one student earns far more pocket money than everyone else, the median describes the group much better.
INVESTIGATION
Try it yourself
Collect 20 real values, such as the number of letters in classmates first names. Draw a dot plot and a box plot, calculate mean, median, IQR and MAD, then write two sentences describing centre and spread.
Watch
Basic Probability
Math Antics · 11:28
A gentle introduction to describing uncertainty and reading data displays.
Before you watch: Which question expects variability: your height, or the heights of your class?
- Which display shows the shape of a distribution best?
- What does the median tell you that the mean does not?
Interactive simulation · PhET
Mean: Share and Balance
Share unequal amounts fairly and watch the balance point of the data set.
While you explore
- Why is the mean called a balance point?
- What happens to the mean, and to the median, when you add one very large value?
Key vocabulary
- Mean absolute deviation
- The average distance of values from the mean.
- Interquartile range
- The spread of the middle half of the data.
- Statistical question
- A question whose answers vary.
Practice questions
0/1 correct
Level 1 · Criterion A
Which question is a statistical question?
MYP criterion tasks
Level 2 · Criterion C
A data set is 3, 4, 4, 5, 20. Compare the mean and median and say which better describes the data.
Reflect & track
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