# 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 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 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 S TATISTICS Section 2-4 Measures of Center

2 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman a value at the center or middle of a data set Measures of Center

3 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values x = n  x x x

6 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definitions  Median the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

8 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 6.72 3.46 3.606.44 3.46 3.60 6.446.72 no exact middle -- shared by two numbers 3.60 + 6.44 2 (even number of values) MEDIAN is 5.02

11 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 6.72 3.46 3.606.44 26.70 3.46 3.60 6.446.72 26.70 (in order - odd number of values) exact middle MEDIAN is 6.44 6.72 3.46 3.606.44 3.46 3.60 6.446.72 no exact middle -- shared by two numbers 3.60 + 6.44 2 (even number of values) MEDIAN is 5.02

12 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman a. 5 5 5 3 1 5 1 4 3 5 b. 1 2 2 2 3 4 5 6 6 6 7 9 c. 1 2 3 6 7 8 9 10 Examples  Mode is 5  Bimodal - 2 and 6  No Mode

14 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman  Midrange the value midway between the highest and lowest values in the original data set Definitions

15 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman use class midpoint of classes for variable x Mean from a Frequency Table

18 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman use class midpoint of classes for variable x Mean from a Frequency Table x = Formula 2-2 f  (f x) 

19 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Weighted Mean x = w  (w x) 

21 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Advantages - Disadvantages Table 2-13 Best Measure of Center

22 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Skewness Mode = Mean = Median SYMMETRIC Figure 2-13 (b)

24 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median Figure 2-13 (b) Figure 2-13 (a)

25 Chapter 2. Section 2-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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)

Download ppt "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."

Similar presentations