Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Statistics Two Meanings Specific numbers Method of analysis 1 Statistics Specific number numerical measurement determined by a set of data Example: Twenty-three percent of people polled believed that there are too many polls. 2 Statistics Method of analysis a collection of methods for planning experiments, obtaining data, and then then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data 3 Statistics Descriptive Statistics • Handles the collection and presentation of data • Inferential Statistics • Analyzing and drawing conclusions from numerical information 4 Definitions Population the complete collection of all elements (scores, people, measurements, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied. 5 Definitions Census the collection of data from every element in a population Sample a subcollection of elements drawn from a population 6 Definitions Parameter a numerical measurement describing some characteristic of a population 7 Definitions Parameter a numerical measurement describing some characteristic of a population population parameter 8 Definitions Statistic a numerical measurement describing some characteristic of a sample 9 Definitions Statistic a numerical measurement describing some characteristic of a sample sample statistic 10 Definitions Quantitative data numbers representing counts or measurements 11 Definitions Quantitative data numbers representing counts or measurements Qualitative (or categorical or attribute) data can be separated into different categories that are distinguished by some nonnumeric characteristics 12 Definitions Quantitative data the incomes of college graduates 13 Definitions Quantitative data the incomes of college graduates Qualitative (or categorical or attribute) data the genders (male/female) of college graduates 14 Definitions Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values 0, 1, 2, 3, . . . 15 Definitions Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values 0, 1, 2, 3, . . . Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps 2 3 16 Definitions Discrete The number of eggs that hens lay; for example, 3 eggs a day. 17 Definitions Discrete The number of eggs that hens lay; for example, 3 eggs a day. Continuous The amounts of milk that cows produce; for example, 2.343115 gallons a day. 18 Definitions nominal level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high) Example: survey responses yes, no, undecided 19 Definitions ordinal level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless Example: Course grades A, B, C, D, or F 20 Definitions interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is no natural zero starting point (where none of the quantity is present) Example: Years 1000, 2000, 1776, and 1492 21 Definitions ratio level of measurement the interval level modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful. Example: Prices of college textbooks 22 Levels of Measurement Nominal - categories only Ordinal - categories with some order Interval - differences but no natural starting point Ratio - differences and a natural starting point 23 Levels of Measurement Nominal - categories only Ordinal - categories with some order Interval - differences but no natural starting point Ratio - differences and a natural starting point 24 Stem-and Leaf Plot Stem Raw Data (Test Grades) 67 72 89 85 88 90 75 89 99 100 6 7 8 9 10 Leaves 7 25 5899 09 0 25 Example: Create a Stem and Leaf Plot for the following data which represents ages of CEO's: 53 45 41 36 55 50 37 48 52 62 43 46 39 50 52 61 48 37 48 55 59 52 39 41 50 The TI-83 will not create the Stem and Leaf Plot for you completely, but it will allow you to sort the data which makes creating the chart by hand easy. Here is what to do: 26 1. Enter the data into a free list (use L1 if it is available). Recall that you do this by hitting STAT, then 1 for Edit and clear L1 if necessary. After you have entered the data into L1 the screen should look like this: 27 2. Now hit 2nd MODE for quit to get to the homescreen. Now hit STAT to get this screen: 3. Now select 2 to get SortA( which stands for Sort Ascending). Your screen will look like this: 28 4. Enter the list you wish to sort in this case L1 (hit 2nd 1). Your screen looks like this 5. Now hit enter, the screen will say done. Hit Stat then edit to get back to the editor. Your data should be sorted. Here is what the screen should look like: 29 Stem Leaf 3 3 67799 4 1135 4 6888 5 00222355 5 9 6 12 30 Definitions Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude 31 Definitions Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude often denoted by x~ (pronounced ‘x-tilde’) 32 Definitions Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude often denoted by x~ (pronounced ‘x-tilde’) is not affected by an extreme value 33 6.72 3.46 3.60 6.44 3.46 3.60 6.44 6.72 (even number of values) no exact middle -- shared by two numbers 3.60 + 6.44 2 MEDIAN is 5.02 34 6.72 3.46 3.60 6.44 3.46 3.60 6.44 6.72 (even number of values) no exact middle -- shared by two numbers 3.60 + 6.44 MEDIAN is 5.02 2 6.72 3.46 3.60 6.44 26.70 3.46 3.60 6.44 6.72 26.70 (in order - exact middle odd number of values) MEDIAN is 6.44 35 Qualitative vs Quantitative • Number of students who turn a paper in late. • Sex of the next baby born in a hospital. • Amount of fluid in a machine to fill bottles of soda pop. • Brand of a personal computer. • Zip Codes. 36 Discrete vs Continuous • Price of a textbook. • The length of a new born baby. • The number of bad checks received by a store. • Concentration of a contaminant in a solution. • Actual weight of a 1-lb can of coffee. 37 Measures of Position Quartiles, Deciles, Percentiles 38 Quartiles Q1, Q2, Q3 39 Quartiles Q1, Q2, Q3 divides ranked scores into four equal parts 25% 25% 25% 25% Q1 Q2 Q3 40 Deciles D1, D2, D3, D4, D5, D6, D7, D8, D9 divides ranked data into ten equal parts 41 Deciles D1, D2, D3, D4, D5, D6, D7, D8, D9 divides ranked data into ten equal parts 10% 10% 10% D1 D2 D3 10% 10% 10% D4 D5 10% 10% 10% 10% D6 D7 D8 D9 42 Quartiles Q1 = P25 Q2 = P50 Q3 = P75 43 • Range The difference between the highest and lowest score • Interquartile Range (or IQR): Q3 - Q1 44 • Interquartile Range (or IQR): Q3 - Q1 • Semi-interquartile Range: (Q3- Q1)/2 • Midquartile: (Q1+ Q3)/2 • 10 - 90 Percentile Range: P90 - P10 • Midrange: (smallest + largest)/2 45 Finding the Percentile of a Given Score Percentile of score x = number of scores less than x • 100 total number of scores 46 Finding the Score Given a Percentile R= k 100 •n n k R Pk total number of values in the data set percentile being used locator that gives the position of a value kth percentile 47 Start Finding the Value of the kth Percentile Sort the data. (Arrange the data in order of lowest to highest.) Compute L= k n 100 ( ) where n = number of values k = percentile in question Is L a whole number ? No Yes The value of the kth percentile is midway between the Lth value and the next value in the sorted set of data. Find Pk by adding the L th value and the next value and dividing the total by 2. Change L by rounding it up to the next larger whole number. The value of Pk is the Lth value, counting from the lowest 48 Stem-and Leaf Plot Stem Raw Data (Test Grades) 67 72 89 88 90 Find P50 P50= 85 75 6 7 8 9 10 89 99 100 k R n 100 50 R 10 5 100 P50= the mean of the 5th and 6th score or 88.5 Find P33 P33= Leaves 7 25 5899 09 0 k R n 100 33 R 10 3.3 100 P33= round up to 4, the fourth score is 85 49 Stem-and Leaf Plot Stem Raw Data 16 19 22 23 24 25 26 27 28 28 29 30 31 31 34 Find P50 P50= k R n 100 50 R 15 7.5 100 P50= round up to 8, the eight score is 27 Find P30 P30= 1 2 3 Leaves 69 234567889 0114 k R n 100 30 R 15 4.5 100 P30= round up to 5, the fifth score is 24 50 Stem-and Leaf Plot Stem Raw Data 16 19 22 23 24 25 26 27 28 28 29 30 31 31 34 What percentile is 30? 11/15 = 73rd percentile 1 2 3 Leaves 69 234567889 0114 What percentile is 22? 2/15 = 13th percentile 51