Distributions & Variation
Look at This Data Display (Set A)
Study the data display and answer the questions about its shape.
| 0–2 goals | |
| 3–4 goals | |
| 5–6 goals | |
| 7–8 goals | |
| 9–10 goals |
Which group has the most teams?
Is the data bunched in the middle or spread out evenly?
Are there any groups with very few teams?
Look at This Data Display (Set B)
Study the data and answer.
| 0–5 min | |
| 6–10 min | |
| 11–15 min | |
| 16–20 min |
Which time range is the most common?
Is the data clustered on one side?
How many people took more than 15 minutes?
Describe the Distribution (Set A)
Circle the best answer.
Most scores are in the middle with fewer at the ends. This is:
When data values are very different from each other, there is:
If every student scored exactly 7/10, the variation is:
Describe the Distribution (Set B)
Circle the best answer.
Most data is on the left side with a 'tail' to the right:
Data is evenly spread across all categories:
One value is much higher/lower than all others:
High or Low Variation? (Set A)
Sort each example.
High or Low Variation? (Set B)
Sort each example.
True or False? (Distributions)
Circle TRUE or FALSE.
If all values are the same, there is no variation
A wider spread of data means more variation
An outlier is a value that fits perfectly with the rest
Most real-world data sets have some variation
Match Data Words to Meanings
Draw a line from each word to its meaning.
Order Data Sets by Variation
Number from 1 (least variation) to 3 (most variation).
Find the Range (Set A)
Calculate the range for each data set. Range = highest − lowest.
Data: 5, 8, 12, 3, 7. Range = ___ − ___ = ___
Data: 20, 25, 22, 28, 21. Range = ___
Data: 100, 50, 75, 90, 60. Range = ___
Find the Range (Set B)
Calculate the range.
Data: 14, 14, 15, 14, 15. Range = ___
Data: 2, 45, 8, 10, 12. Range = ___
Which set above has more variation? How does the range tell you?
Range Calculations
Find the range (total = highest, partA = lowest, partB = range).
Identify Outliers
Circle the outlier (the value that does not fit with the rest).
Data: 10, 12, 11, 13, 50
Data: 80, 82, 5, 79, 81
Data: 25, 27, 26, 28, 25, 90
Identify Outliers (Set B)
Circle the outlier.
Data: 4, 5, 6, 4, 5, 30
Data: 100, 98, 102, 99, 15
Data: 55, 52, 58, 54, 200
Spread and Variation (Set A)
Circle the correct answer.
Data with a SMALL range has:
Data: 5, 6, 7, 5, 6 — the range is:
Data: 10, 50, 20, 80, 30 — the range is:
Which set has MORE variation: {3, 4, 5} or {1, 50, 100}?
Spread and Variation (Set B)
Circle the correct answer.
Data: 20, 22, 21, 19, 20 — the range is:
Data: 8, 35, 12, 40, 5 — the range is:
A set with range 3 has ___ variation than a set with range 50:
Range = Highest − Lowest. If highest = 45 and lowest = 18, range = ?
Range Calculations (Set B)
Range = Highest − Lowest. Total = highest, partA = lowest, partB = range.
Range Calculations (Set C)
Find the missing number.
More or Less Variation?
Sort each data set: more or less variation?
Sort: Cluster or Spread?
Sort each description.
Match Data to Range
Draw a line from each data set to its range.
Match Descriptions to Data
Draw a line to match.
Distribution of Test Scores
Use the graph to answer questions about the distribution.
| 0-5 | |
| 6-10 | |
| 11-15 | |
| 16-20 |
Which score range was most common?
How many students scored 10 or less?
Is the data clustered or spread out?
How many students took the test?
Distribution of Heights
Use the graph to answer.
| 120-129 cm | |
| 130-139 cm | |
| 140-149 cm | |
| 150-159 cm |
Which height range was most common?
Where is the data clustered?
What is the range of the group counts?
Variation in Everyday Life
Think about variation in the real world.
Give an example of data with LOW variation (e.g. temperatures in one day):
Give an example of data with HIGH variation:
Why is it useful to know if data has high or low variation?
Calculate the Range
Find the range for each data set.
Data: 15, 22, 18, 30, 10. Highest = ___, Lowest = ___, Range = ___
Data: 5, 5, 6, 5, 7, 5. Highest = ___, Lowest = ___, Range = ___
Data: 100, 45, 80, 60, 95. Highest = ___, Lowest = ___, Range = ___
Which set above has the most variation? How do you know?
Distribution of Pocket Money
Record the data in a tally chart.
| Item | Tally | Total |
|---|---|---|
$0-$2 | ||
$3-$5 | ||
$6-$8 | ||
$9+ |
Range Patterns
These are ranges for data sets. Continue the pattern.
Describe the Data (Set A)
Look at each set of data and describe the distribution.
Spelling test scores: 4, 5, 7, 7, 8, 8, 8, 9, 9, 10. Where are most scores? Much variation?
Number of books read: 1, 1, 2, 5, 5, 5, 6, 6, 12. Spread out or bunched?
Describe the Data (Set B)
Describe each data set.
Heights (cm): 130, 132, 131, 133, 130, 132. Describe the variation.
Goals scored: 0, 1, 1, 2, 2, 3, 3, 3, 4, 10. Is there an outlier?
Compare Two Data Sets (Set A)
Compare these two sets of data.
Set A: 45, 47, 48, 50, 51, 52, 55. Set B: 20, 35, 48, 50, 63, 78, 95. Which has more variation?
Compare Two Data Sets (Set B)
Compare these data sets.
Class A test scores: 70, 72, 71, 73, 70. Class B test scores: 50, 60, 70, 80, 90. Which class had more consistent results?
Explain what 'consistent results' means using the word 'variation'.
Range as a Measure of Variation
The range = highest value − lowest value.
Data: 3, 7, 12, 5, 9. Range = ___ − ___ = ___
Data: 22, 24, 23, 25, 22. Range = ___
Which data set above has more variation? How does the range help you tell?
What Does the Shape Tell Us?
Circle the best description.
Data: 1, 2, 5, 8, 8, 9, 9, 10. Most values are:
Data: 1, 1, 2, 2, 3, 7, 8, 9. The distribution is:
Data: 5, 5, 5, 5, 5. The shape is:
Investigate Variation
Answer these investigation questions.
If you measured the height of everyone in your class, would you expect high or low variation? Why?
If you rolled a dice 100 times, would you expect each number to appear exactly the same number of times?
Give an example of data you would expect to have very low variation.
Challenge: Create Data Sets
Create your own data sets to match these descriptions.
Write 8 numbers that have LOW variation:
Write 8 numbers that have HIGH variation:
Write 8 numbers with one outlier:
Home Activity: Investigating Variation
Explore variation in data at home!
- 1Measure the temperature at 9 am every day for a week. Is there much variation?
- 2Count how many steps you take to walk to 5 different places. How spread out are the numbers?
- 3Ask 10 people their favourite number between 1 and 10. Are the answers bunched or spread?
- 4Roll a dice 30 times. Do all numbers appear the same amount? Describe the variation.
Understanding the Median
Find the median (middle value) of each dataset.
3, 7, 9, 14, 21 — median = ___
4, 8, 11, 15, 17, 22 — median = ___
24, 16, 9, 31, 7 — first put in order: ___. Median = ___
How does the median help us understand a dataset?
Understanding the Mean (Average)
Find the mean of each dataset.
4, 8, 6, 10, 7 — total = ___, mean = ___
15, 20, 25, 10 — total = ___, mean = ___
Temperatures over 5 days: 18, 22, 25, 21, 19 — mean temperature = ___
Range of a Dataset
Find the range (largest − smallest) of each dataset.
5, 12, 3, 9, 17, 8 — range = ___
24, 16, 32, 9, 41 — range = ___
If a dataset has a large range, what does that tell you about the data?
Sort: Low or High Variation?
Sort each dataset by whether it shows low or high variation.
Interpret Distributions (Set A)
Circle the best description for each dataset.
Test scores: 72, 75, 71, 74, 73, 76. This distribution is:
Heights: 130, 145, 162, 170, 131. This distribution is:
Daily steps: 8000, 8100, 7900, 8050, 8000. This distribution is:
Pocket money: $2, $15, $8, $30, $5. This distribution is:
Describing Distributions
Describe each distribution in your own words.
Daily rainfall (mm): 0, 0, 12, 0, 0, 45, 0, 2, 0, 0. Describe the distribution.
Marks on a test (out of 20): 14, 16, 13, 15, 17, 14, 16, 15. Describe the distribution.
Which dataset has more variation? Explain how you can tell.
Plant Growth Over 5 Weeks
Each leaf icon = 2 cm of growth. Read and answer.
| Week 1 | |
| Week 2 | |
| Week 3 | |
| Week 4 | |
| Week 5 |
In which week did the plant grow the most?
What was the total growth over 5 weeks?
Describe the pattern of growth. Is it consistent?
Calculate the mean growth per week.
Hours of Sleep Survey
10 students recorded how many hours they slept. Read the tally.
| Item | Tally | Total |
|---|---|---|
Less than 8 hours | ||
8 hours | ||
9 hours | ||
More than 9 hours |
Outliers in Data
An outlier is a value that is very different from the others.
Scores: 15, 16, 14, 17, 15, 2, 16. Which score is an outlier? ___. How does it affect the mean?
Masses: 3.2 kg, 3.5 kg, 3.1 kg, 25 kg, 3.4 kg. Circle the outlier. Why might this value be here?
Comparing Two Datasets
Compare these two sets of test results.
Class A: 60, 65, 70, 68, 72, 65. Class B: 45, 80, 55, 90, 40, 88. Find the range for each class.
Which class shows more variation? How do you know?
Find the mean for each class. Which class performed better on average?
Stem-and-Leaf Plots
A stem-and-leaf plot organises data by tens (stems) and ones (leaves).
Data: 23, 25, 31, 35, 38, 42, 44, 45, 51. Complete the stem-and-leaf plot: 2|___ 3|___ 4|___ 5|___
What is the median of this dataset?
Describe the distribution — is the data spread or clustered?
Challenge: Making Predictions
Use data distributions to make predictions.
A shop sells 30, 45, 38, 50, 42 ice creams on 5 days. Predict sales for day 6. Justify your prediction.
If a new data point of 100 is added to the set, how would the mean and range change?