Unit 4: Probability and Statistics
This unit is devoted to statistics, a branch of mathematics concerned with representation, analysis, and interpretation of data. It also involves the study of probability, which is the analysis of outcomes of random events.
Completing this unit should take you approximately 11 hours.
Upon successful completion of this unit, you will be able to:
- analyze graphic presentations of data (histograms, bar graphs, circle graphs, pictographs, line plots, tables, etc);
- calculate range, mean, median, and mode of data sets;
- interpret measures of central tendency and dispersion;
- solve for probability using counting procedures, tables, and tree diagrams;
- appraise how the presentation and selection of data leads to different or inappropriate interpretations; and
- infer and analyze conclusions from sample surveys, experiments, and observational studies.
4.1: Data Representation
This section demonstrates different ways of representing data.The term "data" can be applied to any collection of numbers. It is difficult to interpret the trends in data when the numbers are written down simply as a list. This is why it is convenient to represent data visually in different kinds of graphs and charts. Watch this introductory video and complete the interactive exercises.
- One of the ways to organize data is a stem-and-leaf plot. Watch the video and complete the interactive exercises.
This lecture series describes other ways to represent data on a graph: pictographs and bar graphs. A histogram is a type of bar graph. Watch the videos and complete the interactive exercises.
Sometimes it is helpful to know how many times a given data point occurs in the set of numbers. This is easy to find out if the data is organized in a frequency table or a dot plot. Watch the video and complete the corresponding interactive exercises.
- This video compares different ways of representing data and discusses how to determine which way is best for a particular type of data.
- Complete the interactive exercises to practice analyzing data represented in different ways.
While graphs provide a convenient visual representation of data, you can also use them to manipulate perception. It is essential to pay attention to the scales on a graph's axes and its other features to reach correct conclusions. This video shows an example of a misleading comparison between two graphs.
4.2: Measures of Central Tendency
Summarizing quantitative data can be done by calculating measures of central tendency (the central, or most commonly occurring, points in the data) and measures of dispersion. Measures of central tendency are discussed in this section.
As the name suggests, measures of central tendency describe the center, or the middle point, of the data. The most common measure of central tendency is average, or arithmetic mean. Other measures include median and mode. Watch this lecture series and complete the interactive exercises.
This lecture series discusses using mean and median to make inferences about data points and how the small changes in data can affect mean and median. Watch the videos and complete the interactive exercises.
- Complete these exercises and check your answers.
4.3: Measures of Dispersion
Measures of dispersion, also referred to as measures of spread, indicate how far the data points are from the central points and one another.
This lecture series discusses measures of dispersion (interquartile range, variance, and standard deviation). Watch these videos and complete the interactive exercises.
4.4: Counting and Probability
The term "probability" is often used when discussing an event that might or might not happen. A real-life event probability, or chance of this event happening, usually depends on many factors and is difficult to calculate. In this section, you will learn to find probabilities of simple events, such as getting a specific number when rolling a die or getting several heads in a row when tossing a coin.
This lecture series introduces the concept of probability and gives examples of calculating basic probability. Watch the videos and complete the interactive exercises.
The probabilities of simple events can be combined, or compounded, to find the probability of two or more events happening. When outcomes of these events don't depend on each other, the events are considered independent. This lecture series presents examples of calculating compound probabilities of independent events using diagrams. Watch the videos and complete the interactive exercises.
Watch this lecture series to see more various examples of calculating probabilities of independent and dependent events. When the outcome of one event depends on the outcome of another, the events are considered dependent. Complete the interactive exercises
- Complete these exercises and check your answers.
4.5: Collecting Data
Before you can represent data, you have to collect it in some way. This section discusses different ways of collecting data and how they can affect the conclusions obtained from data analysis.
This lecture series discusses the studies conducted using surveys. You can use surveys to obtain information about a group of people, but it can be impossible to survey each person if the group is very large. The limited number of people surveyed is called a sample. The way a sample is selected can affect the outcome of a study and its validity. Watch the videos and complete the interactive exercises.
This lecture series discusses the difference between observational studies and experiments and the conclusions you can draw from each.
- Read this section, which discusses potential biases in experimental design and ethical issues that may arise when conducting experimental studies.
- Complete these exercises and check your answers.
Unit 4 Assessment
- Receive a grade
Take this assessment to see how well you understood this unit.
- This assessment does not count towards your grade. It is just for practice!
- You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.