Statistics

Compare Distributions

1

Tally the Results

A class voted for their favourite sport. Complete the tally chart.

ItemTallyTotal
Cricket
Football
Swimming
Tennis
2

Favourite Pets

Use the picture graph to answer the questions.

Dogs
Cats
Fish
Birds
1

Which pet is the most popular?

2

How many more students chose dogs than fish?

3

How many students were surveyed in total?

3

Favourite Fruits

Complete the tally chart for favourite fruits.

ItemTallyTotal
Apple
Banana
Grapes
Watermelon
4

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 = ___

5

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 = ___.

6

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 = ___

7

Match Statistic to Description

Draw a line to match each statistic to what it tells you.

Mean
Median
Mode
Range
Most common value
Middle value when ordered
Spread of the data
Average value
8

Data Display Questions

Circle the best display for each purpose.

Showing exact vote counts:

Bar graph
Pie chart
Line graph

Showing change over time:

Bar graph
Pie chart
Line graph

Showing parts of a whole:

Bar graph
Pie chart
Line graph
9

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:

10

Interpret the Data

Based on the class data above.

Higher median score?

Class A
Class B
The same

Highest individual score?

Class A
Class B
The same

Lowest individual score?

Class A
Class B
The same
11

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? ___

12

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?

13

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?

14

Outlier Questions

Circle the correct answer.

An outlier is:

Most common value
Value far from the rest
Middle value

Data: 5, 6, 7, 8, 50. The outlier is:

5
7
50

Outliers affect the ___ most:

Mean
Median
Mode
15

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.
16

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 = ___

17

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): ___

18

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: ___

19

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:

15
17
20

Mode:

3
4
5

Median:

4
5
6

Range:

3
4
7
20

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: ___

21

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: ___

22

Match Statistical Question to Best Display

Draw a line to match each question to the best data display.

Track scores over time
Compare categories at one time
Show distribution of individual values
Show proportion of a whole
Pie chart
Line graph
Dot plot/stem-leaf
Bar graph
23

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? ___

24

Sort: Which Average is Best?

Sort each situation into the most appropriate average to use.

House prices in a suburb
Most popular shoe size
Average rainfall per month
Salary survey with outliers
Test scores (evenly spread)
Most common colour of cars
Use Mean
Use Median
Use Mode
25

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: ___

26

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
1

Which city has the greater temperature range?

2

What is the mean January temperature for both cities combined?

3

How many degrees warmer is Sydney than Melbourne in July?

27

Number of Books Read Per Month

Complete the tally chart for books read by a class.

ItemTallyTotal
0 books
1–2 books
3–4 books
5+ books
28

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? ___

29

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? ___

30

Reading Graphs

Answer these graph interpretation questions.

A bar graph is best for:

Continuous data over time
Comparing categories
Showing distribution

A line graph is best for:

Showing change over time
Comparing categories
Showing each data point

The mode is shown most easily by:

Mean calculation
Stem-and-leaf
Median calculation

To find the median in a stem-and-leaf plot:

Find middle value after ordering
Add all values and divide
Find most common