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Statistics_3_2

# Statistics_3_2 - Chapter 3 Data Description 31 Measures of...

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Chapter 3: Data Description 3–1 Measures of Central Tendency 3–2 Measures of Variation 3–3 Measures of Position 3–4 Exploratory Data Analysis

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3-1 Measures of Central Tendency A statistic is a characteristic or measure obtained by using the data values from a sample. A parameter is a characteristic or measure obtained by using all the data values from a specific population. The Mean .
Example: The data represent the number of days off per year for a sample of individuals selected from nine different countries. 20, 26, 40, 36, 23, 42, 35, 24, 30 Find the mean. Solution: The procedure for finding the mean for grouped data uses the midpoints of the classes. Example: The data represent the number of miles run during one week for a sample of 20 runners. Find the mean. Solution: Step 1 Find the midpoints of each class. Step 2 Multiply the frequency by the midpoint.

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Step 3 Divide the sum by n to get the mean. The Median The median is the midpoint of the data array. The symbol for the median is MD. Step 1 Arrange the data in order. Step 2 Select the middle point.
Example: The number of rooms in the seven hotels in downtown Pittsburgh is 713, 300, 618, 595, 311, 401, and 292. Find the median. Solution: Step 1 Arrange the data in order. 292, 300, 311, 401, 595, 618, 713 Step 2 Select the middle value, 401. Example: Find the median for the daily vehicle pass charge for five U.S. National Parks. The costs are \$25, \$15, \$15, \$20, and \$15. Solution: .

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Example: The number of cloudy days for the top 10 cloudiest cities is shown. Find the median. 209, 223, 211, 227, 213, 240, 240, 211, 229, 212 Solution: Arrange the data in order, The Mode The value that occurs most often in a data set is called the mode.
Example: Find the mode of the signing bonuses of eight NFL players for a specific year. The bonuses in millions of dollars are 18.0, 14.0, 34.5, 10, 11.3, 10, 12.4, 10 Solution: arrange the data in order 10, 10, 10, 11.3, 12.4, 14.0, 18.0, 34.5 The mode is 10. Example: Find the mode for the number of coal employees per county for 10 selected counties in southwestern Pennsylvania. 110, 731, 1031, 84, 20, 118, 1162, 1977, 103, 752 Solution: there is no mode.

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Example: The data show the number of licensed nuclear reactors in the United States for a recent 15-year period. Find the mode. 104 104 104 104 104 107 109 109 109 109 109 110 111 111 112 Solution: we have two modes 104 and 109. Example: Find the modal class for the frequency distribution of miles that 20 runners ran in one week, Solution: The mode could also Be given as the midpoint 23 miles
Notice: The mode is the only measure of central tendency that can be used in finding the most typical case when the data are nominal or categorical. The mean, median, and mode can be quite different

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Statistics_3_2 - Chapter 3 Data Description 31 Measures of...

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