Compare Distributions
Tally the Results
A class voted for their favourite sport. Complete the tally chart.
| Item | Tally | Total |
|---|---|---|
Cricket | ||
Football | ||
Swimming | ||
Tennis |
Favourite Pets
Use the picture graph to answer the questions.
| Dogs | |
| Cats | |
| Fish | |
| Birds |
Which pet is the most popular?
How many more students chose dogs than fish?
How many students were surveyed in total?
Favourite Fruits
Complete the tally chart for favourite fruits.
| Item | Tally | Total |
|---|---|---|
Apple | ||
Banana | ||
Grapes | ||
Watermelon |
Calculate the Mean
Find the mean (average) of each data set.
Data: 4, 6, 8, 10, 12. Mean = ___
Data: 3, 5, 7, 9, 11. Mean = ___
Data: 10, 20, 30, 40, 50. Mean = ___
Find the Median and Mode
Find the median and mode.
Data: 3, 5, 5, 7, 9. Median = ___. Mode = ___.
Data: 2, 4, 4, 4, 8, 10. Median = ___. Mode = ___.
Data: 12, 15, 18, 20, 25. Median = ___. Mode = ___.
Find the Range
Find the range (highest − lowest).
Data: 5, 8, 12, 15, 20. Range = ___
Data: 22, 35, 40, 55, 68. Range = ___
Data: 3, 3, 7, 9, 11, 15. Range = ___
Match Statistic to Description
Draw a line to match each statistic to what it tells you.
Data Display Questions
Circle the best display for each purpose.
Showing exact vote counts:
Showing change over time:
Showing parts of a whole:
Compare Two Classes
Class A scores: 65, 70, 72, 75, 80, 82, 85, 90. Class B scores: 55, 60, 75, 78, 80, 85, 88, 95.
Range of Class A: ___
Range of Class B: ___
Which class has greater spread? ___
Which class performed more consistently? Explain:
Interpret the Data
Based on the class data above.
Higher median score?
Highest individual score?
Lowest individual score?
Compare Two Sports Teams
Team A scores: 3, 5, 2, 4, 6, 3, 5, 4. Team B scores: 1, 7, 0, 8, 2, 6, 3, 5.
Team A mean = ___. Team B mean = ___.
Team A range = ___. Team B range = ___.
Which team is more consistent? ___
Describe the Distribution
Heights (cm): 140, 142, 145, 145, 148, 150, 150, 152, 155, 160.
Describe the distribution (shape, spread, centre):
What if a 180 cm student joined? What is this called?
Choosing the Right Average
Explain which average is best.
House prices: $400K, $420K, $450K, $480K, $2M. Which average and why?
Shoe sizes sold in a shop. Which average and why?
Outlier Questions
Circle the correct answer.
An outlier is:
Data: 5, 6, 7, 8, 50. The outlier is:
Outliers affect the ___ most:
Home Activity: Data Collector
Collect and compare data at home!
- 1Survey your family about their favourite meal. Display in a bar graph.
- 2Record temperature each day for a week. Describe the distribution.
- 3Compare page counts of 5 books. Find the range and median.
- 4Calculate mean, median and mode of ages in your family.
Mean, Median, Mode and Range — Extended
Calculate all four measures for each data set.
Data: 8, 3, 7, 3, 9, 6, 5. Mean = ___. Median = ___. Mode = ___. Range = ___
Data: 12, 15, 11, 18, 15, 20, 14, 15. Mean = ___. Median = ___. Mode = ___. Range = ___
Data: 2, 7, 4, 9, 4, 6, 4, 8, 3. Mean = ___. Median = ___. Mode = ___. Range = ___
Stem-and-Leaf Plots
Read this stem-and-leaf plot and answer the questions. Stem | Leaves 3 | 2 4 6 7 4 | 1 1 3 8 9 5 | 0 2 5
Minimum value: ___. Maximum value: ___. Range: ___
Median: ___
Mode: ___
Mean (show working): ___
Frequency Tables
Use this frequency table to answer the questions. Score: 1, 2, 3, 4, 5. Frequency: 3, 5, 8, 6, 3.
Total number of data values: ___
Mode: ___
Mean score: ___
Median score: ___
Interpreting Dot Plots
A dot plot shows: • at 3 (3 dots), 4 (5 dots), 5 (4 dots), 6 (3 dots), 7 (2 dots).
Total data values:
Mode:
Median:
Range:
Comparing Two Distributions — Box Plots
Box plot summaries: Class A: Min=45, Q1=60, Median=72, Q3=80, Max=95 Class B: Min=50, Q1=65, Median=75, Q3=85, Max=100
Range of Class A: ___. Range of Class B: ___
Inter-quartile range of Class A: ___. Class B: ___
Which class performed more consistently overall? Explain: ___
Constructing a Stem-and-Leaf Plot
Create a stem-and-leaf plot for this data: 23, 31, 45, 28, 37, 41, 52, 34, 46, 29, 38, 43.
Stem | Leaves 2 | ___ 3 | ___ 4 | ___ 5 | ___
Median: ___. Range: ___. Mode: ___
Match Statistical Question to Best Display
Draw a line to match each question to the best data display.
Effect of Adding a Value
Data set: 5, 8, 9, 6, 7. Mean = 7, Median = 7, Mode = none.
Add the value 100. New mean: ___. New median: ___. Which changed more? ___
Add the value 7. New mean: ___. New median: ___. New mode: ___
Which average is most affected by extreme values? ___. Why? ___
Sort: Which Average is Best?
Sort each situation into the most appropriate average to use.
Collecting and Displaying Data
Design a data collection and display.
Write a question to collect numerical data: ___
Describe how you would collect 20 data values: ___
Choose the best display and explain why: ___
Weekly Temperature Comparison
This graph compares mean weekly temperatures for two cities (each icon = 2°C). Answer the questions.
| Sydney — Jan | |
| Melbourne — Jan | |
| Sydney — July | |
| Melbourne — July |
Which city has the greater temperature range?
What is the mean January temperature for both cities combined?
How many degrees warmer is Sydney than Melbourne in July?
Number of Books Read Per Month
Complete the tally chart for books read by a class.
| Item | Tally | Total |
|---|---|---|
0 books | ||
1–2 books | ||
3–4 books | ||
5+ books |
Drawing Conclusions from Data
Answer these questions about drawing conclusions.
Quiz scores: Class 6A mean = 72, Class 6B mean = 75. Can you conclude 6B is smarter? Explain: ___
Why is it important to look at both the centre AND the spread of data? ___
How could two data sets have the same mean but look very different? ___
Statistical Investigation
Conduct a mini statistical investigation.
Question: Which number appears most when rolling a die? Prediction: ___
Roll a die 20 times. Results: ___ Mode: ___. Mean: ___. Range: ___
Was your prediction correct? What did you learn? ___
Reading Graphs
Answer these graph interpretation questions.
A bar graph is best for:
A line graph is best for:
The mode is shown most easily by:
To find the median in a stem-and-leaf plot: