Statistics for Decision- Making in Business - Maricopa Community ...

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2.3 Descriptive Statistics – Center and Position Histograms provide us with a great visualization of the overall distribution of values. A distribution describes the layout of the values of a quantitative or categorical variable. To further describe the differences between two similar distributions, it is helpful to use statistics that describe center, location, and spread. 2.3.1 Mean and Median To make peace with some regularly occurring notation in statistics, we will use mean “the sum of.” For instance, (“sigma”) to Let‟s say that we have a set of variable values. To distinguish each of these “ ‟s” we‟ll use subscripts, denoting them: Then, to indicate that we want to sum these values across all subscripts, we would write: Which means, “sum up all values in the dataset,” or Using this new notation, we already know how to calculate the mean: Mean – x-bar notation The mean value, or average, of a dataset containing values can be written as: ̅, is used to denote the mean of a sample and can be read as “x-bar.” A common point of confusion for students is the difference in the subscript and the denominator . Many people think that the subscript should be to match the number of elements in the dataset. However, specifically refers to the very last value in the dataset. We treat the as an index that goes across all subscripts from 1 all the way up to and including . To Statistics for Decision-Making in Business © Milos Podmanik Page 56
̅ ̅ account for this discrepancy, mathematicians usually write where the index should start below sigma and the maximum value above the sigma. For example, if there are 3 values in the dataset, we would write the mean as: As you can see, the sigma notation can quickly become convoluted, and so we typically just write to indicate the sum of all -values. Median The median value of a dataset is the value that represents the physical center of the data set. To locate the median: Organize the data values from smallest to largest. Then, If there is an odd number of values in the data set, the center value can be located by counting in positions from the smallest value, including the smallest value. Alternatively, one can count in an equal number of values from the left and right endpoints to locate the center value. If there is an even number of values in the data set, average the two middle-most values together. The locations of the two middle-most values are: Positions from the smallest value, including the smallest value. Once again, these values can be found by counting from the left and the right endpoints of the dataset. Example 1: Find the mean and median salaries for the company represented by the following dataset (in thousands). Explain which measure better reflects the overall company demographic. SOLUTION: We first find the mean: This means that, on average, employees earn $148,200 per year. Statistics for Decision-Making in Business © Milos Podmanik Page 57
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Statistics for Decision- Making in
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A Note to Students This book is far
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3.4 Conditional Probability In many
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That is, the probability that the c
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This can happen in one of two ways:
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f. All numerical red cards are remo
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3.5 Combinations and Permutations R
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Combination - Order Does NOT Matter
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1. Are repeats/replacements allowed
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Object 4 Object 5 Also notice that
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e. 2. Your classmate was absent whe
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3.6 Expected Value Imagine that you
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An expected value is actually not s
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Where The expected value is: , - (
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SOLUTION: We first note that there
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Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Statistics for Decision-Making in B
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For men, we see that the most frequ
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So, we had 10 trials and wanted to
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Example 1: A fair-two sided coin is
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( ) ( ) ( ) ( ) Example 2: A fair,
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Expected Value of a Binomial Random
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f. What is the probability that g.
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Probability For instance, we see th
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Density 0.25 Time Speng Waiting in
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Suppose we wish to find ( ), that i
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Density Resulting in a standard dev
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Density Without going into detail h
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a. What is the probability that the
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Statistics for Decision-Making in B
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As you can see, this is a difficult
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We wish to know the area of the sha
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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following data was collected on the
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DULY CAUTIONED: The assumptions her
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Homework Problems -6.2 1. In a samp
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Hypothesis Test Conclusion Test Say
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Hypothesis Test Conclusion Since yo
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SOLUTION: d. A generic conclusion s
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9. Based on the “Structure of a H
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1.2 Descriptive VS. Inferential Sta
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Relative Frequency 35% 30% 25% 20%
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Repair Cost Mean 971 Standard Error
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Probability Pizza Size Distribution
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