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1 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

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Presentation on theme: "1 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY."— Presentation transcript:

1 1 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 2-4 Measures of Center

2 2 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman a value at the center or middle of a data set Measures of Center

3 3 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Mean (Arithmetic Mean) AVERAGE the number obtained by adding the values and dividing the total by the number of values Definitions

4 4 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Notation  denotes the addition of a set of values x is the variable usually used to represent the individual data values n represents the number of data values in a sample N represents the number of data values in a population

5 5 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values x = n  x x x

6 6 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Notation µ is pronounced ‘mu’ and denotes the mean of all values in a population is pronounced ‘x-bar’ and denotes the mean of a set of sample values Calculators can calculate the mean of data x = n  x x x N µ =  x x

7 7 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definitions  Median the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

8 8 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman 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’) ~

9 9 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman 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 ~

10 10 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman no exact middle -- shared by two numbers (even number of values) MEDIAN is 5.02

11 11 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman (in order - odd number of values) exact middle MEDIAN is no exact middle -- shared by two numbers (even number of values) MEDIAN is 5.02

12 12 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definitions  Mode the score that occurs most frequently Bimodal Multimodal No Mode denoted by M the only measure of central tendency that can be used with nominal data

13 13 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman a b c Examples  Mode is 5  Bimodal - 2 and 6  No Mode

14 14 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman  Midrange the value midway between the highest and lowest values in the original data set Definitions

15 15 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman  Midrange the value midway between the highest and lowest values in the original data set Definitions Midrange = highest score + lowest score 2

16 16 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Carry one more decimal place than is present in the original set of values Round-off Rule for Measures of Center

17 17 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman use class midpoint of classes for variable x Mean from a Frequency Table

18 18 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman use class midpoint of classes for variable x Mean from a Frequency Table x = Formula 2-2 f  (f x) 

19 19 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman use class midpoint of classes for variable x Mean from a Frequency Table x = class midpoint f = frequency  f = n f = n x = Formula 2-2 f  (f x) 

20 20 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Weighted Mean x = w  (w x) 

21 21 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Advantages - Disadvantages Table 2-13 Best Measure of Center

22 22 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman  Symmetric Data is symmetric if the left half of its histogram is roughly a mirror of its right half.  Skewed Data is skewed if it is not symmetric and if it extends more to one side than the other. Definitions

23 23 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Skewness Mode = Mean = Median SYMMETRIC Figure 2-13 (b)

24 24 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median Figure 2-13 (b) Figure 2-13 (a)

25 25 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median SKEWED RIGHT (positively) Mean Mode Median Figure 2-13 (b) Figure 2-13 (a) Figure 2-13 (c)


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