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# STAT 110: Notes for Week of 9/13/16 STAT 110

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This 4 page Class Notes was uploaded by runnergal on Sunday September 18, 2016. The Class Notes belongs to STAT 110 at University of South Carolina taught by Dr. Wilma J. Sims in Fall 2016. Since its upload, it has received 5 views. For similar materials see Introduction to Statistical Reasoning in Statistics at University of South Carolina.

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Date Created: 09/18/16

STAT 110: Notes for Week of 9/13/16 Chapter 10 o In order to describe data, you must figure out if it is quantitative or categorical. o Quantitative Variable: a variable that measures something already in numerical form, ex. inches of a piece of paper, weight of a person, IQ, etc. o Categorical Variable: measures something that needs to be put into categories and/or given numerical value, ex. favorite color, ethnicity, current feelings, etc. o Distribution of a variable: tells what values of a variable occur and how often they occur, ex. 20 people like the color blue, 0 people like the color orange, etc. Distributions can be described through tables, graphs, or numerical summaries. o Frequency table: gives the count of how many times a value appears in a distribution, ex. 0 people like the color orange. o Relative Frequency: gives the proportion (often a percentage or fraction) of how many times a value appears in a distribution compared to the total amount of values, ex. 0 people out of 200 students in this class like the color orange, or 0%. o Roundoff Errors: occurs in tables when values are rounded off. This means that when you add all of the values together, you will not reach the true sum. This usually occurs in distributions with large values. o Pie Chart: used for categorical variables. This type of graph shows the amount of data that belongs to each category. It can only be used when the data represents a whole, ex. 0 orange + 20 blue + 180 garnet = 200 students. The wedges of the “pie” should be proportional to one another. o Bar Graph: used for categorical variables. Represents how much data is in each category by presenting proportional bars. The categories of the variable are on the horizontal (flat) axis. The frequencies of the categories (how many people/things are in each category) are on the vertical (tall) axis. The categories of a bar graph do not have to be parts of a whole, unlike pie charts. o Pictogram: a bar graph that uses images instead of bars. The bars of a pictogram must only increase by height, not width, in order to not confuse the interpreters. o Line Graph: used for quantitative variables. This graph shows how a variable changes over time. Time is on the horizontal axis. The frequencies of the variable are on the vertical axis. Look for trends (overall patterns) that go up or down in the line graph. Look for deviations (major differences) from the overall pattern, also known as spikes (higher than the overall pattern) or plunges (lower than the overall pattern). Look for seasonal variation: deviations that happen in a pattern over a certain amount of time, ex. more babies are born in September than any other month every year. Check the scales on line graphs – the amount of space between the times on the horizontal axis as well as the amount of space between the frequencies on the vertical axis can drastically change what the graph looks like. Chapter 11 o Histogram: used for quantitative data. This type of graph shows distribution. It looks like a bar graph with no spaces between the bars. The variable scale is on the horizontal axis, ex. GPA. The frequency is on the vertical axis, ex. 25 people. Each bar represents a different class, ex. 0.0-0.99, 1.0-1.99, 2.0-2.99, 3.0- 3.99. The base of the bar represents the width of the class, ex. all of the values between 2.0 and 2.99. The height of the bar represents frequency, ex. 25 people have a GPA between 2.0-2.99. There is no space between the bars, unless there are no values in a certain class. o Interpreting Histograms Symmetric Distribution: when the left and right sides of the histogram are perfectly symmetrical. This is very rare. Skewed Distribution: when one side of the histogram from the center holds more data than the other side. Skewed to the right: the right side of the histogram is longer than the left side. Skewed to the left: the left side of the histogram is longer than the right side. Outlier: a value in the distribution that is outside of the normal data pattern.

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