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Chapter 3- Statistics for Business and Economics

Chapter 3- Statistics for Business and Economics - LEARNING...

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3-1 LEARNING OBJECTIVES LO1. Calculate the arithmetic mean, weighted mean, median, and mode . LO2. Explain the characteristics, uses, advantages, and disadvantages of each measure of location . LO3. Identify the position of the mean, median, and mode for both symmetric and skewed distributions . LO4. Compute and interpret the range, mean deviation, variance, and standard deviation . LO5. Understand the characteristics, uses, advantages, and disadvantages of each measure of dispersion . LO6. Understand Chebyshev’s theorem and the Empirical Rule as they relate to a set of observations.
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3-2 Population Mean For ungrouped data, the population mean is the sum of all the population values divided by the total number of population values:
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3-3 EXAMPLE – Population Mean There are 12 high schools in the Corry County School District. Listed below is the number of students enrolled in each. Is this information a sample or a population? What is the arithmetic mean number of students per high school? Answer: This is a population because we are considering all the high schools in the Corry County School District.
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3-4 Sample Mean For ungrouped data, the sample mean is the sum of all the sample values divided by the number of sample values: LO1
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3-5 EXAMPLE – Sample Mean SunCom is studying the number of minutes used by clients in a particular cell phone rate plan. A random sample of 12 clients showed the following number of minutes used last month. What is the arithmetic mean number of minutes used? LO1
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3-6 Example – Sample Mean Loyola University wants to know the average age of its student body. We take a sample by asking everyone in this class their age. 19 21 20 18 28 18 20 22 19 19 19 + 20 +18 + 21…+ 19 60 x _ X = Would this be a good estimate of the average age at Loyola?
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3-7 Weighted Mean The weighted mean of a set of numbers X 1 , X 2 , ..., X n , with corresponding weights w 1 , w 2 , ..., w n , is computed from the following formula: LO1
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3-8 EXAMPLE – Weighted Mean The Carter Construction Company pays its hourly employees $16.50, $19.00, or $25.00 per hour. There are 26 hourly employees, 14 of which are paid at the $16.50 rate, 10 at the $19.00 rate, and 2 at the $25.00 rate. What is the mean hourly rate paid the 26 employees? LO1
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3-9 EXAMPLES - Median The five-year annualized total returns of the ten top-performing diversified mutual funds for the period ending March 2009 are listed below. What is the median annualized return of these funds? LO1
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3-10 EXAMPLES - Median The number of mutual funds listed is an even number (10). These funds are already ordered from largest to smallest, so we can easily find the middle two returns.
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