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Intro to Statistics

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### Section 1

1. 1. CHAPTER 1 Exploring Data
2. 2. Displaying Distributions with Graphs What Graphs to Use When
3. 3. VOCABULARY <ul><li>Individuals – objects described by a set of data. They may be people, but they may be animals or things. </li></ul><ul><li>Variable – any characteristic of an individual. </li></ul>
4. 4. TYPES OF VARIABLES <ul><li>Categorical – groups or categories an individual belongs to (job title, gender, etc.) </li></ul><ul><li>Quantitative – numerical values for which it makes sense to do arithmetic operations on (height, weight, income, etc.) </li></ul>
5. 5. WAYS TO DISPLAY DATA <ul><li>Dotplot </li></ul><ul><li>Histogram </li></ul><ul><li>Bar Chart </li></ul><ul><li>Stemplot </li></ul><ul><li>Timeplot </li></ul><ul><li>Boxplot and Modified Boxplot </li></ul><ul><li> Let’s look at the first three. </li></ul>
6. 6. DOTPLOT <ul><li>Drawing a horizontal line to represent the variable </li></ul><ul><li>Make a number scale for the values of the variable. </li></ul><ul><li>Mark a dot at the appropriate place for each observation </li></ul>
7. 7. HISTOGRAM <ul><li>Used when variables take many values </li></ul><ul><li>Group values of the variables together </li></ul><ul><li>Most common graph used with one quantitative variable </li></ul>
8. 8. BAR CHART <ul><li>Used when data is categorical </li></ul><ul><li>Not used until later in Statistics course </li></ul>
9. 9. INTERPRETING DISTRIBUTIONS Learning How to CUSS
10. 10. CUSS <ul><li>C – give the center of the distribution (value that divides the observations so that half are above and half are below) </li></ul><ul><li>U – give any unusual features of the distribution (outlier, gap, multiple peaks) </li></ul><ul><li>S – give the spread of the graph (use range = largest value – smallest value) </li></ul><ul><li>S – give the shape of the graph </li></ul>
11. 11. CUSS Continued <ul><li>Outlier – an individual observation that falls outside the overall pattern of the graph. (unusual feature) </li></ul><ul><li>Possible shapes </li></ul><ul><ul><li>Symmetric – if the right and left sides are approximately mirror images of each other </li></ul></ul><ul><ul><li>Skewed to the right – the right side of the distribution extends out further to the right </li></ul></ul><ul><ul><li>Skewed to the left – the left side of the distribution extends out further to the left </li></ul></ul>
12. 12. EXAMPLE <ul><li>Center – </li></ul><ul><li>Unusual Features – </li></ul><ul><li>Spread – </li></ul><ul><li>Shape – </li></ul>
13. 13. EXAMPLE <ul><li>Center – the center is approx. 13% </li></ul><ul><li>Unusual Features – there are possible outliers and two gaps </li></ul><ul><li>Spread – the range is approx. 16 </li></ul><ul><li>Shape – close to symmetric without outliers </li></ul>
14. 14. ASSIGNMENT <ul><li>Page 8-9 #1.1 - 1.3 </li></ul><ul><li>Page 15-18 #1.4 – 1.8 </li></ul><ul><li>CUSS Worksheet </li></ul>
15. 15. STEMPLOTS <ul><li>Used with small data sets </li></ul><ul><li>Made by separating each observation into a stem , consisting of all but the rightmost digit, and a leaf , the final digit. </li></ul><ul><li>Preserves the actual value of each observation. </li></ul>3 | 4, 6 4 | 3 5 | 2, 4, 5, 7, 8 6 | 0, 0, 1, 2, 4, 4, 4, 5, 6, 9 7 | 0, 1, 3, 4, 6, 7, 8, 8 8 | 1, 1, 2, 3, 3, 6, 7, 8, 9, 9 9 | 7
16. 16. VARIATION OF A STEMPLOT <ul><li>Called split stems </li></ul><ul><li>Each stem appears twice </li></ul><ul><li>Leaves 0 to 4 go on the upper stem </li></ul><ul><li>Leaves 5 to 9 go on the lower stem </li></ul>1 | 0,1,1,3 1 | 8, 9, 9, 9, 9, 9 2 | 0, 0, 1,2,2,4 2 | 5,7,7,9 3 | 0, 1 3 | 5,5,6
17. 17. TIMEPLOT <ul><li>Plots each observation against the time at which it was measured </li></ul><ul><li>Time scale is the horizontal axis </li></ul><ul><li>Variable of interest is the vertical axis </li></ul><ul><li>Look for trends, or overall patterns </li></ul>
18. 18. ASSIGNMENT <ul><li>Page 18-22 #1.9 – 1.13 </li></ul><ul><li>Page 24-28 #1.16, 1.17, 1.20, 1.21 </li></ul><ul><li>Smokers vs. Ex-Smokers Worksheet </li></ul><ul><li>Prepare for Quiz 1.1 </li></ul>