DOC PREVIEW
VCU STAT 210 - Lecture11(4) (1)

This preview shows page 1-2-3-4-5-34-35-36-37-68-69-70-71-72 out of 72 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 72 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Slide 1Practice ProblemsAdditional Reading and ExamplesTest 2Slide 5Motivating ExampleSlide 7Measures of Central LocationMeasures of Central LocationMeasures of Central LocationSlide 11B. Measures of SpreadMeasures of SpreadExample 17Example 17B. Measures of SpreadB. Measures of SpreadMeasures of SpreadSample Standard DeviationSample Standard DeviationSample Standard DeviationSample Standard DeviationSample Standard DeviationSample Standard DeviationSample Standard DeviationVarianceVarianceExample 18Example 18Example 18Standard DeviationStandard DeviationExample 19Example 19Example 19Example 19Measures of SpreadMeasures of SpreadMeasures of SpreadMeasures of SpreadIQRIQRIQRIQRIQRIQRIQRIQRIQRIQRExample 20Example 20Example 20Example 20Example 20Example 20Example 21Example 21Example 21Example 21Example 21Example 21Example 21Slide 65TI-83/84 CalculatorMotivating ExampleMotivating Example SolutionExample - AnswersExample - AnswersExample - AnswersSlide 72STAT 210Lecture 11 Measures of SpreadSeptember 21, 2016Practice ProblemsPages 94 through 97Relevant problems: IV.3, IV.4, IV.5, IV.6 (a) and (c), and 11 (c)Recommended problems: IV.4, IV.6 (c) and IV.11 (c)Additional Reading and ExamplesPages 90 through 93Test 2Monday, September 26Questions for the first 10 minutes, then test – papers due promptly at the end of class!Covers chapters 3 and 4 (pages 43 – 97)Combination of multiple choice questions and short answer questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerMotivating ExampleA statistics course at a large university provides free statistics review sessions that students can use to answer questions, with help solving problems, and with help studying for tests. The course instructor is interested in the mean number of students who attend all review sessions held for this statistics course, and selects a sample of 15 review sessions spread out over a month’s time. The number of students who attended these 15 review sessions is as follows. How would you describe the spread of this sample of data?6 1 8 3 1 5 11 7 4 28 12 9 2 10 13ClickerMeasures of Central Location1. Mean (Average)The population mean is denoted by the Greek letter m (read “mu”) and is the sum of all observations divided by how many individuals that there are in the population. This is (usually) an unknown parameter.Measures of Central LocationThe population mean is estimated by the sample mean, denoted by X (read “X-bar”).X = S x = x1 + x2 + x3 + … + xn n nThis is a statistic.Measures of Central Location2. MedianThe population median is usually denoted by the Greek letter h (read “eta”), and is estimated by the sample median, denoted by M. The median is the central value with half of the observations less than it and half of the observations greater than it.ClickerB. Measures of SpreadIf all the values of a characteristic are the same then the characteristic is a constant, and both the mean and median are the constant value. There is no spread in the data.If, however, all the values are not the same, then the characteristic is called a variable and of interest is to measure the amount of spread (or dispersion or variability) around a central value.Measures of Spread1. Range = maximum value - minimum valueThe range is a measure of overall variation, not variation around a central value. The range will be heavily influenced by outliers.Example 17Without 391:The smallest observation is 113 and the largest observation is 222.So the range is 222 - 113 = 109.Example 17With 391:The smallest observation is 113 and the largest observation is 391.So the range is 391 - 113 = 278.The range went from 109 to 278 due to the existence of one outlier.B. Measures of Spread2. Standard DeviationThe standard deviation is a measure of variability around the mean.A deviation is the amount that an observation differs from the mean: x – X.B. Measures of Spread2. Standard DeviationThe standard deviation is a measure of variability around the mean.The population standard deviation is denoted by s (read “sigma”).Measures of Spread2. Standard DeviationThe standard deviation is a measure of variability around the mean.The population standard deviation is denoted by s.Since all subjects of the population are rarely known, the population standard deviation is usually unknown and must be estimated by the sample standard deviation, denoted S.Sample Standard DeviationS = S (x - X)2 n - 1Sample Standard Deviation1. Calculate the sample mean X.Sample Standard Deviation1. Calculate the sample mean X.2. Compute the n deviations from the mean: x - X.The sum of the deviations (x - X) will always equal 0.S (x - X) = 0Sample Standard Deviation1. Calculate the sample mean X.2. Compute the n deviations from the mean: x - X.3. Square each deviation: (x - X)2.Sample Standard Deviation1. Calculate the sample mean X.2. Compute the n deviations from the mean: x - X.3. Square each deviation: (x - X)2.4. Sum the squared deviations: S (x - X)2.Sample Standard Deviation1. Calculate the sample mean X.2. Compute the n deviations from the mean: x - X.3. Square each deviation: (x - X)2.4. Sum the squared deviations: S (x - X)2.5. Divide this sum by n - 1: S (x - X)2 n - 1 The divisor n - 1 is called the degrees of freedom.Sample Standard Deviation1. Calculate the sample mean X.2. Compute the n deviations from the mean: x - X.3. Square each deviation: (x - X)2.4. Sum the squared deviations: S (x - X)2.5. Divide this sum by n - 1: S (x - X)2 n - 16. Take the square root of the above number.VarianceA measure of spread around the mean that is related to the standard deviation is the variance. The population variance is denoted by s2 (read “sigma squared”) and since the entire population is usually unknown the population variance is estimated using the sample variance s2.s2 = S (x - X)2 n - 1VarianceThe population variance is estimated using the sample variance s2.s2 = S (x - X)2 n – 1The standard deviation is preferred to the variance because while the standard deviation is measured in the units of the original data, the variance is measured in the units squared.Example 18From example 13, the sample mean is X = 162.625.Example 18x x - X (x - X)2128 128-162.625 = -34.625 1198.89150 150-162.625 = -12.625 159.39183 183-162.625 =


View Full Document

VCU STAT 210 - Lecture11(4) (1)

Documents in this Course
Lecture32

Lecture32

57 pages

Lecture31

Lecture31

84 pages

Lecture29

Lecture29

26 pages

Lecture28

Lecture28

63 pages

Lecture27

Lecture27

73 pages

Lecture26

Lecture26

78 pages

Lecture25

Lecture25

86 pages

Lecture24

Lecture24

54 pages

Lecture22

Lecture22

30 pages

Lecture21

Lecture21

76 pages

Lecture20

Lecture20

71 pages

Lecture19

Lecture19

78 pages

Lecture17

Lecture17

54 pages

Lecture16

Lecture16

59 pages

Lecture15

Lecture15

40 pages

Lecture14

Lecture14

80 pages

Lecture11

Lecture11

68 pages

Lecture10

Lecture10

46 pages

Lecture9

Lecture9

45 pages

Lecture7

Lecture7

67 pages

Lecture5

Lecture5

44 pages

Lecture3

Lecture3

32 pages

Lecture2

Lecture2

64 pages

Load more
Download Lecture11(4) (1)
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture11(4) (1) and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture11(4) (1) 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?