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

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If the deviations are small (good thing!), then the squared deviations will be small, and so the sum of squares will be small. This implies a small deviation. So, a large standard deviation means that there is a lot of variability, or that the values are vastly different from one another. A small standard deviation means the values in the data set are quite alike. In the near future, you'll see why it is important to have a small standard deviation. In general, as the variance and standard deviation get larger, our ability to make precise statements about the population quickly evaporates. We will be using variance and standard deviation consistently for the rest of the semester. It is important to get comfortable with it. 2.4.3 Do Population Variances and Standard Deviations Fall into Play Indeed they do. Do you think that we can find them Definitely not! The population variance requires the use of the population mean, . How do we get We take the average of all the values in the entire population. Since we typically don't know this value, we also typically don't know the population variance, so certainly we don't know the population standard deviation (since it's the square root of the population variance). The table below summarizes the notations we need to recognize: Sample Population Variance Standard Deviation The population parameter, , is the lowercase Greek letter “Sigma.” (This is as opposed to the sample statistic, .) 2.4.4 Interquartile Range The standard deviation, much like the mean, is easily skewed by excessively small or large values. We noticed this in the first example in this section. Using the idea of medians and percentiles is a safe bet for outlier-proofing our spread estimates. An interquartile range is the difference between the 3 rd quartile and the 1 st quartile. Remember, these are simply the 75 th and 25 th percentiles, respectively. The difference is the middle 50% of the dataset. Statistics for Decision-Making in Business © Milos Podmanik Page 70
This gives us a nice measure of how spread out the data is about the median. Example 2: Consider the following home prices and find both the standard deviation and the interquartile range. Describe what conclusions can be drawn from these values. Values (thous. $) 95 875 96 89 87 88 93 91 SOLUTION: Using Excel, we find the following: The standard deviation indicates that home prices, on average, vary by $277,100 from the mean value. However, we see from the interquartile range that the middle 50% of homes only vary by $6,500. The standard deviation is being skewed by the home that is priced at $875,000. The interquartile range tells us that the majority of home values stay pretty close to the median value. Additionally, we see that most home values are between $88,000 and $96,000. 2.4.5 Descriptive Statistics: Analysis ToolPak in Excel To generate most of the features we have discussed up until now, we turn to Excel‟s Analysis ToolPak for a more automated approach. Let‟s consider the house data above: Statistics for Decision-Making in Business © Milos Podmanik Page 71
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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For the present time, we‟ll proce
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Row Labels Average of Revenue ($) M
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Page 81 and 82: Chapter 3 Probability and Decision
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Combination - Order Does NOT Matter
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1. Are repeats/replacements allowed
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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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Density Resulting in a standard dev
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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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Thus, we need to find the lower and
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√ The lower limit is: √ And the
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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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Since this is a mathematical questi
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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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Symmetric: 35 30 25 20 15 10 5 0 10
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Repair Cost Mean 971 Standard Error
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Probability Pizza Size Distribution
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