STA-Ch3_Data_Description-2 - Outline Introduction Measures of Central Tendency Chapter 3 Measures of Variation Data Description Measures of Position 1

STA-Ch3_Data_Description-2 - Outline Introduction Measures...

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1 Chapter 3 Chapter 3 Data Description Data Description 2 Outline Outline circle5 Introduction circle5 Measures of Central Tendency circle5 Measures of Variation circle5 Measures of Position 3 Objectives Objectives circle5 Summarize data using the measures of central tendency , such as the mean, median, mode. circle5 Describe data using the measures of variation , such as the range , standard deviation and coefficient of variation. circle5 Identify the position of a data value in a data set using various measures of position, such as percentiles, quartiles and z-scores 4 Measures of Central Tendency Measures of Central Tendency circle5 A statistic statistic is a characteristic or measure obtained by using the data values from a sample circle5 A parameter parameter is a characteristic or measure obtained by using the data values from a specific population
5 The Mean (arithmetic average) circle5 The mean mean is defined to be the sum of the data values divided by the total number of values circle5 The mean, in most cases, is not an actual data value circle5 We will compute two means: one for the sample and one for a finite population of values 6 The Sample Mean The Sample Mean n X n X X X X n = + + + ... = 2 1 X The symbol represents the sample mean. is read as “X-bar”. The Greek symbol is read as “sigma” and it means “to sum” X The Sample Mean The Sample Mean -ExampleExampleweeksnXXThe ages in weeks of a random sample of six kittens at an animal shelter are 3, 8, 5, 12,14 and 12Find the average age of this sampleThe Population MeanThe Population Mean 8
93-121220,000$=59,000+9,000+12,000+20,000+50,000==NXμA small company consists of the owner, the manager, the salesperson, and two technicians. The salaries are listed as $50,000, $20,000, $12,000, $9,000 and $9,000 respectively (Assume this is the population)Then the population mean will be:10MDMDThe Median The Median -Example Example circle5The weights (in pounds) of seven soldiers are 180, 201, 220, 191, 219, 209, and 186. Find the mediancircle5Arrange the data in order and select the middle point The Population Mean - Example Example - The Median The Median circle5 When a data set is ordered, it is called a data array data array circle5 The median median is defined to be the midpoint of the data array circle5 The symbol used to denote the median is 12
13 The Median The Median circle5 In the previous example, there was an odd number odd number of values in the data set circle5 In this case it is easy to select the middle number in the data array 14 The Median The Median circle5 When there is an even number even number of values in the data set, the median is obtained by taking the average average of the two middle numbers of the two middle numbers

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