✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2 - Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3 - Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5 - Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Is AP Statistics Hard? Is AP Statistics Worth Taking?
Best Quizlet Decks for AP Statistics
⏱️ 4 min read
June 3, 2020
Before taking you on the journey of learning, statistics, let's make some sense of data.
Data is actually in plural form; it contains information about individuals or units that have characteristics, also called variables. The values that variables assume are called data. Since the variables can be categorical or quantitative, data can also be divided into categorical and quantitative. When the variable assumes values that are attributes, we call the variable categorical, and data as categorical—for example, the colors of cars, names of states, districts, countries. The values for colors of cars may stretch from white to black, any possible color you may see on the street. Then it makes sense to group those values and compare them. When we measure a characteristic that results in numerical values, then we deal with quantitative variables and subsequently with quantitative data—for example, the number of days, the price of the product, the age of the individuals. The quantitative data divided further into two types: discrete and continuous. Recall your algebra class when we called discrete to those numbers that were whole and continuous to those numbers that come in the intervals. The price, weight, age are continuous because it can assume numbers in intervals. When data assumed are numbers, then it makes sense to find an average.
The variables can be measured at different levels: nominal, ordinal, interval, and ratio. The qualitative variables are nominal and ordinal. The difference between the two is that ordinal has some order between qualitative data, but nominal has not. For example, the satisfaction level of customers can be ranked by some order from most to least. The difference between interval and ratio is that interval level measurement ranks data, but there is no meaningful 0, whereas the ratio has 0 in its meaning.
Sometimes the variables can be either categorical or quantitative. Depending on your interest in the study, you will need to make a decision on how to treat them.
The variables change from one individual to another, and so data change over time. If we ask the same question to different people we’ll get different answers. Statistics tools will help us notice the relationships and varied patterns among individuals. This variability makes the study of statistics more interesting.
Let's look at this example to see how well we can make a distinction between the two types of variables and data. In the example below we can learn more about variables.
The chart shows the number of job-related injuries in each of the transportation industries in 1998.
Industry Number of injuries
Intercity bus 5100
1. What are the variables that we are studying?
Looking at the table, we can see that we have two variables; type of industry and number of injuries.
2. Categorize each variable as quantitative or qualitative.
The type of industry, of course, is a qualitative variable, as the values are names for transportation. At the same time, the number of job-related injuries is quantitative, as the values are numbers.
3. Categorize each quantitative variable as discrete or continuous.
The number of job-related injuries is discrete.
4. Identify the level of measurement for each variable.
The type of industry is nominal, and the number of job-related injuries is a ratio.
5. The railroad is shown as the safest transportation industry. Does that mean railroads have fewer accidents than the other industries? Explain.
This question makes you think about what the number means to you. The railroads do show fewer job-related injuries; however, there may be other things to consider. For example, railroads employ fewer people than the other transportation industries in the study.
6. From the information given, comment on the relationship between the variables.
We can see that the railroads have the fewest job-related injuries. In contrast, the airline industry has the most job-related injuries (more than twice those of the railroad industry). The numbers of job-related injuries in the subway and trucking industries are fairly comparable.
Bottom line: always look at data and see what you can see behind, how they are related, and how they compare to each other.
🎥Watch: AP Stats - Unit 1 Streams
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