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STA309 Exam I Outline

# STA309 Exam I Outline - STA309 Exam 1 Examining...

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STA309 Exam 1 Examining distribution with graphs Variables: the characteristics of the individuals. Individuals may be people or objects. A variable can take different values for different individuals. o Types of variables: Quantitative variables: takes numerical values for which arithmetic makes sense. Examples: class size, height, pulse, haircut cost, money in coins Categorical variables: record which category a person or thing falls into. Examples: gender, feelings about class Distributions: Describes a variable’s pattern of variation. Tells the values of the variable and how often they occur. o Why is there variation? Individuals vary. Measurement errors. Categorical variables : o Distribution lists the categories and gives either the count or the percent of individuals in each category: o Pie charts help us see what part of the whole each group forms o Bar charts: Height of the bars shows the counts (or percents) in the categories Quantitative variables o Histograms : Divide the range of data into classes of equal width. Count the number of observations in each class Draw the histogram with height equal to the count. In excel: Rows cases Columns variables Bin the center point of the interval; type in numbers you want for the range and select that column To make bars touch, click on bar and select “format data series” Use excel only for shape; data very wrong; esp. 1 st interval Descriptive stats: skewness (+) right skewed; (-) left skewed; > 1 pretty skewed o Stem plots : Separate each observation into a Stem - all but final digit Leaf – the final digit Write the stems from top (smallest) to bottom (largest) Write each leaf to the right of the stem in increasing order. Advantages of Stem plots: Used for small data sets. Quicker to make. Presents more detailed information. o Time plots : Illustrates measurements taken over time X-axis - time Y-axis- measurement. Used to describe trends, seasonality, fluctuations, and cycles Examining distributions : Look for the overall pattern and striking deviations from the pattern (such as outliers) o Use histograms and stemplots to describe: Shape Symmetric - right and left sides are approximately mirror images (don't expect perfection in real data) Skewed - one tail extends longer than the other side o Right skewed means long tail on right (quite common) o Sometimes you may have to omit outliers (b/c they could be incorrect) Center Spread Bimodal: two humps (ex. Old Faithful’s eruptions) Describing distributions with Numbers: Measuring the Center: o Median: The median is the midpoint of a distribution. Half of the observations are smaller. Half of the observations are larger. To find the median: 1. Arrange all observations in ascending order.

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STA309 Exam I Outline - STA309 Exam 1 Examining...

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