Data and Probability

Objective

A. Data Representation and Analysis Students should be able to:

1. distinguish between types of data (qualitative and quantitative data, discrete and continuous data)

2. represent numerical data diagrammatically (stem-and-leaf diagrams and box-and-whisker plots)

3. outline the relative advantages and disadvantages of stem-and-leaf diagrams and box-and-whisker plots in data analyses

4. interpret stem-and-leaf diagrams and box-and-whisker plots

5. determine quartiles and percentiles from raw data, grouped data, stem-and-leaf diagrams, box-and-whisker plots

6. calculate measures of central tendency and dispersion (mode, median, range, interquartile range, semi-interquartile range, variance and standard deviation of grouped and ungrouped data)

7. explain how the standard deviation measures the spread of a set of data

B. Probability Theory Students should be able to:

1. distinguish among the terms experiment, outcome, sample space and event

2. calculate the probability of event A, P(A), as the number of outcomes of A divided by the total number of possible outcomes, when all outcomes are equally likely and the sample space is finite

3. use the basic laws of probability:

(i) the sum of the probabilities of all the outcomes in a sample space is equal to one;

(ii)

Study Resources

• Textbook 12.1
• Video showing how to construct a stem-and-leaf diagram
• Video showing how to construct and interpret a box-and-whisker plot
• Textbook 12.4, 12.5, & 12.6
• Textbook 12.4, 12.5, & 12.6
• Video showing how to interpret a stem-and-leaf diagram
• Video showing how to construct and interpret a box-and-whisker plot
• Textbook 12.4, 12.5, & 12.6
• Video showing how to determine percentiles from raw data, grouped data, and stem-and-leaf diagrams. Note that students should already know how to find quartiles based on their CSEC work; also, the box-and-whisker plot only shows quartiles and the median, so one cannot find additional percentiles from a box-and-whisker plot.
• Textbook 12.3, 12.5, 12.6, 12,8, 12.10
• Video showing how to calculate variance and standard deviation from a list of data
• Video showing how to calculate mean, variance and standard deviation from ungrouped data presented in a table
• Textbook 12.2, 12.3, 12.7, 12.8, & 12.9
• Video 1: Basic introduction about what the standard deviation indicates about the spread of data.
• Video 2: Summarizes meaning of standard deviation and provides one example
• Video 3: One more example of using standard deviation in a problem.
• Textbook 12.10

• Textbook 13.1
• Textbook 13.2
• Textbook 13.2
• Textbook 13.3
• Textbook 13.4
• Textbook 13.5
• Textbook 13.6
• Textbook 13.6
• Textbook 13.7

for any event A

(iii) P(A') = 1 - P(A), where P(A') is the probability that event A does not occur;

4. Use

to calculate probabilities.

5. identify mutually exclusive events A and B such that

6. calculate the conditional probability P(A|B) where

7. identify independent events

8. use the property

or P(A|B) = P(A) where A and B are independent events

9. construct and use possibility space diagrams, tree diagrams and Venn diagrams to solve problems involving probability