Chapter 1 Learning Objectives PDF
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Marian University
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This document provides learning objectives for chapter 1 on data representation and analysis. It covers individuals and variables along with categorical vs quantitative data and different methods to represent such data such as bar charts and histograms. It also includes interpretation of histograms and time plots.
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Chapter 1: Intro and Displaying Data with Graphs Learning Objectives LO 1. Individuals and Variables 1. Individuals: objects described in a set of data a. May be people, animals, plants, or things 2. Variables: any property that characterizes an individual a. Can tak...
Chapter 1: Intro and Displaying Data with Graphs Learning Objectives LO 1. Individuals and Variables 1. Individuals: objects described in a set of data a. May be people, animals, plants, or things 2. Variables: any property that characterizes an individual a. Can take different values for different individuals b. Ex: age, gender, blood pressure, blood type, leaf length, flower color c. Can be quantitative or categorial d. n: number of individuals in sample or population LO 2. Categorial vs Quantitative Data 1. Quantitative: some quantity is assessed or measured for each individual (average can then be reported) a. Ex: age (in years), blood pressure (in mmHg), leaf length (in cm) 2. Categorical: some characteristic describing each individual that can be reported or counted as a proportion of individuals with that characteristic a. Ex: gender (male, female), blood type (A, B, AB, O), flower color (white, red) LO 3. Ways to Chart Categorical Data: Bar Graphs and Pie Charts 1. Bar Graph: each characteristic, or level, is represented by a bar with the height of the bar representing either the frequency or relative frequency a. Frequency: count of individuals with that characteristic b. Relative Frequency: percent of individuals with that characteristic 2. Pie Charts: represent how one categorical variable breaks down its components a. Each characteristic is represented by a slice, and the size of a slice represents what percent of the whole is made up by that characteristic LO 4. Ways to Chart Quantitative Data: Histograms and Dot Plots 1. Histogram: summary graph for a single variable that is useful to understand the pattern of variability, especially for large data sets 2. Dot Plot: graph of the raw data that is useful to describe patterns of variability, especially for small data sets a. To make a dot plot: i. Create a single axis representing the quantitative variable’s range ii. Represent each data point as a dot positioned according to its numerical value iii. When two or more data points have the same value, stack them up LO 5. Interpreting Histograms 1. How to Make a Histogram a. Horizontal Axis: the range of values that the quantitative variable takes is divided into equal size intervals/classes b. Vertical Axis: represents frequency (counts) or relative frequency (percents of total) c. For each class on the horizontal axis, draw a column i. The height of the column represents the count or percent of data points that fall in that class interval 2. The graphs for frequency and relative frequency have identical shapes, but a different count 3. In choosing histogram classes, there are four guidelines a. Not too many classes with either 0 or 1 counts (pancake) b. Not overall summarized that you lose all the information (skyscraper) c. Not so detailed that is no longer a summary (pancake) d. Start with 5 to 10 classes, then refine class choice 4. Histogram Shape: unimodal, bimodal, symmetric, skewed, and irregular a. Symmetric: left half of shape is a mirror image of the right half (ideal; classic) b. Skewed: one side extends farther out than the other side c. Not all distributions have a simple shape 5. Histogram Center: approximate midpoint 6. Histogram Spread: range of values taken 7. Outlier: observations that lie outside the overall pattern of a distribution a. Look for them and try to explain them b. The largest observation is not necessarily an outlier LO 6. Graphing Time Series: Time Plots 1. Time Plot: graph with a sequence for the horizontal variable, like time a. Line connecting the points helps emphasize any change/data collected over time b. Horizontal axis is time, and vertical axis is variable of interest c. Look for a trend and cyclical variations i. Cyclical Variations: variations with some regularity over time
