1. Constructing and Interpreting Visual Displays of Data
“Air bags have saved more lives than seatbelts alone.”
“Post-secondary education will land you a good job.”
“Football (soccer) is the most widely played sport in the world.”

2. Constructing and Interpreting Visual Displays of Data
How can these statements be made?
What must be done before such statements can be made?
Data must be:
Collected
Organized
Clearly displayed
Analyzed

3. Constructing and Interpreting Visual Displays of Data
THE POWER OF INFORMATION:
Use graphics to make data more meaningful (picture is worth a thousand words)
Develop significant conclusions about a data set
State, support, and refute conclusions based on data
Explore some misuses of data
Use correlation coefficients and scatter plots to describe the relationship b/t two variables

4. Constructing and Interpreting Visual Displays of Data
Statistics
Descriptive statistics
Methods used for collecting, presenting, and characterizing a set of data to describe the various features of that entire data set.
You are simplifying and summarizing a large amount of data into a smaller set of numbers (i.e.mean, standard deviation, or graph)
Example: finding average monthly temperature or graphing temperature changes

5. Constructing and Interpreting Visual Displays of Data
Inferential Statistics
Methods used to make an estimation of a characteristic of a population based only on sample results
You are extrapolating from a small amount of data to a larger one
Example: an opinion poll

6. Constructing and Interpreting Visual Displays of Data
Definitions
Population ≡ refers to the entire group about which data are being collected
Data ≡ information providing the basis of a discussion from which conclusions may be drawn; often in form of numbers that can be displayed graphically or in a table
Parameter ≡ a summary measure used to describe a characteristic of the entire population
Statistic ≡ a summary measure that is computed to describe a characteristic from a sample of the population

7. Constructing and Interpreting Visual Displays of Data
Sample ≡ part of a population that is selected to gain information about the whole population
Frequency ≡ the number of times an event occurs or the number of items in a given category
Frequency Table ≡ table listing a variable together with the frequency of each value

8. Constructing and Interpreting Visual Displays of Data
Common Graphical Forms to Represent Data:
Frequency Distribution or Histogram
Stem and Leaf Plot
Pictograph
Circle Graph
Box & Whisker Plot

9. Constructing and Interpreting Visual Displays of Data
Creating a Frequency Table
Pretend you know (remember) the day of the week you were born
Data:

10. 1.1 Constructing and Interpreting Visual Displays of Data
Creating a frequency table (cont)

11. Constructing and Interpreting Visual Displays of Data
Bar Graph – discrete data (data that is not continuous)
Ex. Day of week that students were born

12. Constructing and Interpreting Visual Displays of Data
Histograms are different from bar graphs.
A histogram is a frequency distribution where the horizontal axis is divided into equal class intervals (widths) & the heights of the bars represent the frequencies associated with the corresponding intervals.
Data is continuous (hence the intervals)

13. Constructing and Interpreting Visual Displays of Data
Equal widths
Continuous
Frequency

14. Constructing and Interpreting Visual Displays of Data
Recall-to make a frequency table:
Set up a table using reasonable class intervals
Limit intervals to b/t 5 and 20 depending on amount and spread of data
Make all intervals the same width
Choose intervals so there are no gaps and no piece of data falls in two different classes
Record the number of observations in each class interval.
Include a column for relative frequency total.

15. Constructing and Interpreting Visual Displays of Data
Stem and Leaf Plot
Used for organizing numerical data
Separate each observation into a stem-and-leaf, the stem may have as many digits as needed, but each leaf contains only one digit
Write the stem in a vertical column with the smallest at the top; draw a vertical line at the right of this column
Write each leaf in the row to the right of its stem, in an increasing order
Example: heights of students in centimetres

16. Constructing and Interpreting Visual Displays of Data
Stem & Leaf Plot

17. Constructing and Interpreting Visual Displays of Data
Pictograph
Symbolic representation of data.
Often found in the press or magazines.
Not as credible as other types of graphs.
Difficult to be made accurately.

18. Constructing and Interpreting Visual Displays of Data
Example of Pictograph

19. Constructing and Interpreting Visual Displays of Data
Circle graph (pie chart)
Circle divided into sectors whose areas are proportional to the variables represented.
Central angle determines the size of each sector
Central angle ≡ percentage of data for each sector multiplied by 360º

20. Constructing and Interpreting Visual Displays of Data
Example of Circle Graph

21. Constructing and Interpreting Visual Displays of Data
Box and Whisker Plot
Horizontal representation of the spread of a distribution.
How to make a plot:
Find the overall median (middle ordered number)
Find the upper and lower medians
The box is created by marking the medians (3) on a number line.
The whiskers are created by extending lines to the upper and lower extreme values on the number line.

22. Constructing and Interpreting Visual Displays of Data

23. Constructing and Interpreting Visual Displays of Data

24. Constructing and Interpreting Visual Displays of Data
Broken Line Graph
Created by joining data points with line segments.
Assists in determining models or trends of data

25. Constructing and Interpreting Visual Displays of Data