Unit 1: Exploring One-Variable Data

Statistics is all about data. We explore data, we describe data, we collect data, we test data, and finally, we make inferences about data. This is the first unit, and we begin by exploring data-the descriptive statistics. In this unit, you will distinguish between categorical (a.k.a. qualitative) and quantitative data and learn a variety of tools to display, describe, and compare them.

1.0 Unit 1 Overview: Exploring One-Variable Data

Browse slides from the stream 'Normal Distributions.'

1 min read

57:38

Normal Distributions

We will break down every aspect about the normal curve and how its understanding is essential to any student who aims to be successful on the AP Statistics exam.

Apr 13 2020

• 149 views

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Presentation Slides, Normal Distributions

Apr 13 2020

46:04

Normal Curve and Normal Calculations

Perform normal calculations, learn about the standard normal distribution along with the empirical rule and end with assessing normality.

Oct 18 2019

• 332 views

36:30

Describing Location in a Distribution

Learn how to measure position using percentiles, create and interpret cumulative relative frequency graphs, transform data and how to define and describe density curves.

Oct 11 2019

• 360 views

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Describing Location in a Distribution - Slides

Browse slides from the stream 'Describing Location in a Distribution,' where we cover topics including Exploring Data.

Oct 11 2019

33:46

Displaying Quantitative Data with Graphs

We will discuss how to display quantitative data with different types of graphs and how to describe them.

Sep 27 2019

• 466 views

📄slides

Analyzing Categorical Data - Slides

Browse slides from the stream 'Analyzing Categorical Data,' where we cover topics including Exploring Data.

Sep 18 2019

33:54

Analyzing Categorical Data

Identify different types of data and how we analyze each type.

Sep 18 2019

• 1.1k views

Depending on how we use data, the study of statistics is divided into two main areas: descriptive and inferential. In descriptive statistics, we describe a situation by collecting, organizing, summarizing, and presenting the data. In inferential statistics, we try to make an inference from our collected data to populations by generalizing, estimating, testing, and making predictions. We will preserve the inferential statistics for the future and will focus on the descriptive branch of statistics here.

1.1 Introducing Statistics: What Can We Learn from Data?

Before taking you on the journey of learning, statistics, let's make some sense of data.

1.2 The Language of Variation: Variables

Apr 17 2020

Data can be enormous and hard to understand. For this purpose, statistics was created to help us organize and analyze data. The first values are organized in the tables. Then data are graphed in different displays. Tables are a necessary step to start analyzing data, but it may fail to highlight essential features with data. The graphical displays are visually attractive, easy to read, and see important patterns of the distribution. For categorical variables, the choices are limited. Bar graphs and Pie charts are the most common displays.

1.3 Representing a Categorical Variable with Tables

Apr 17 2020

To construct a bar graph (bar chart), we mark the frequencies on a vertical axis and the categories on the horizontal axis. Each category represents one bar. The frequency of each category determines the heights of the bars. All bars have the same width and gap between adjacent bars. To keep it short, here is the bar graph of stress on the job. We can also use relative frequencies or percentages to construct the bar graph. You can be creative and color each category with a different color. It will be visually attractive and easier to compare them.

1.4 Representing a Categorical Variable with Graphs

Apr 17 2020

This section describes how we organize and display quantitative data. The frequency table is a bit complicated for quantitative data, especially if we deal with vast amounts of data. The good news is that AP doesn’t require you to make one, so we will skip this one. Just know that many computer programs, including our mighty Excel, and your TI series calculator can make it in seconds. The main displays we will discuss are histograms, polygons, ogive, stem-and-leaf plots, and dot-plot.

1.5 Representing a Quantitative Variable with Graphs

Once we organized the set of data of our interest into a certain display of our choice, the next task is to describe the data. In other words we should tell what we see. There are three things that we should look for and never forget it. The three things are shape, center and spread. Let's discuss one by one.

1.6 Describing the Distribution of a Quantitative Variable

3 min read

Statistics is a measure taken from the sample to help us analyze the data. The parameter is the measure taken from the population. In inferential statistics, we will use statistics to make inferences about the parameters. But let’s not jump in there and focus on summary statistics. Mean, median, standard deviation, IQR, range, all are summary statistics for a quantitative variable. The mean median, quartiles, and percentiles measure the center and position for quantitative data, whereas the range IQR, and standard deviation measure the variability for quantitative data. The summary measures change if we convert them to different units.

1.7 Summary Statistics for a Quantitative Variable

This section represents summary statistics for quantitative data graphically. Describing summary statistics we can use it to talk about our data in the context.

1.8 Graphical Representations of Summary Statistics

We talked a lot about distributions and how to describe, summarize and represent them, now it is time to put more into practice by comparing the multiple sets of data. Comparing sets of histograms and boxplots, the above information would come alive to you.

1.9 Comparing Distributions of a Quantitative Variable

This section introduces you to z-scores. When I think of statistics, one of the first things that come in my mind is standard deviation and z-scores. So what are the z-scores? z-scores measure the distance of a value from the mean in standard deviations. The formula is simple but very powerful. It is resistant to units, and it can be used to compare any activity.

1.10 The Normal Distribution