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.”

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

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

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

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

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

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

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

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

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

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

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)

Constructing and Interpreting Visual Displays of Data Equal widths Continuous Frequency

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.

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

Constructing and Interpreting Visual Displays of Data Stem & Leaf Plot

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.

Constructing and Interpreting Visual Displays of Data Example of Pictograph

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

Constructing and Interpreting Visual Displays of Data Example of Circle Graph

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.

Constructing and Interpreting Visual Displays of Data

Constructing and Interpreting Visual Displays of Data

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

Constructing and Interpreting Visual Displays of Data