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# Test 1 Study Guide (with notes!) 220

JMU

GPA 3.5

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## Popular in Elementary Statistics

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This 3 page Study Guide was uploaded by Jay Ty on Thursday September 8, 2016. The Study Guide belongs to 220 at James Madison University taught by Colleen Watson in Fall 2016. Since its upload, it has received 8 views. For similar materials see Elementary Statistics in Math at James Madison University.

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Date Created: 09/08/16

9/1/2016-9/15/2016 Study Guide I. Chapter 2.1 Displaying Categorical Data a. Variable- characteristic that changes from thing to thing b. Data sets can be: i. Categorical: Qualitative, like “words” gender, color of car, zip code, movie ages, yes or no, etc. ii. Numerical: Quantitative 1. Discrete: counting/integers (age rounded by years), money, no way to get a more precise numerical amount 2. Continuous: measurements or the potential for decimals a. Ex: height, volume, weight, age (in length of time) c. Can use frequency distribution i. Frequency distribution (FreQ) Is a table listing all categories and corresponding counts ii. Bar chart, or pie chart (pg. 41) d. Relative frequency (RelFreQ): ???????????????? i. where n equals the sample size (can also be turned into a %) ???? e. Bar chart: a graph of the freQ or RelFreQ i. To make an effective one, it needs: 1. Spaces between bas 2. All bars must be equal width, as shown below (taken from Google) II. Chapter 2.2/2.3 a. Display Numerical Data i. Always looking for spread, numerical values, clumps, gaps, etc. 1. Dot Plots: put a dot for each data point above the number line a. Best for discrete data with small spread b. It is comparative: do 2 graphs to the same number line 2. Stem-n-leaf a. 2 digit numbers b. Stem= tens c. Leaf= ones i. The book practices some 3 digit numbers of highland d. It is comparative: Share the stem, where the leaves (ones) go from the right (right skew) and left (slightly left skew) 3. Histograms a. Similar to a bar chart but it’s numerical i. Usually data needs to be grouped into intervals (classes, bins) ii. It is all continuous data iii. It is all spread out discrete data iv. Rare case: discrete data with a tiny spread, does not need grouping b. Guidelines to grouping for histograms i. # of intervals √ ???? where n equals sample size ????????????−???????????? ii. Width of interval = count by… # ???????? ???????????????????????????????????? iii. Start at the minimum, usually iv. Don’t start at zero unless you have it in your data!!! III. Chapter 3.1 a. Knowing the mean (or median) is only half the story and is useless without a measure of variation b. Box Plots i. Mean= spread/standard deviation ii. Median= Inter Quantile Range 1. ???? − ???? 3 1 2. ???? =3Upper quantile= Median upper half of data 3. ???? =1Lower Quantile 4. Percentile: Percentage in which you do better than 84 percentile (means you did better than 84% of the population being calculated) 5. Whiskers: Whiskers extend to the highest/lowest data points that are NOT already outliers (whiskers do not) cross fences iii. Clues to the Right Skew 1. Right whisker is longer than the left 2. Median is to the left of the center of the box 3. If there are outliers, they are on the right iv. Know how to do this on SPSS!!! (Look at your own worksheets!) IV. Chapter 3.2 Standard Deviation a. It is the spread that goes with the mean ∑(????−????????????????) 2 i. Sample Standard Deviation: √ where n= sample size and s ????−1 = ???? equals the standard deviation 2 ii. Population Standard Deviation √ ∑(????−????) where ???? is the population ???? = ???? mean, n is the sample size, and ???? is the standard deviation iii. Standard deviation: “typical” or average amount on a data point is away from the mean iv. Area under curve= probability= proportion = % v. Empirical Rule: Helps us estimate areas of unimodal/symmetric curves 1. It is a rule that states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts: 68% of data falls within the first standard deviation from the mean. 95% fall within two standard deviations. 2. It looks something like this (only for these percentages, ignore the 2.4 to 4.8) For extra practice, look at the word problem in the book and that she provides. I will not put her own content and practice questions in this study guide! Good luck with your studies!

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