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

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We begin by listing them in ascending order: The two middle values are 48 and 50 (these values are four values in from either side). These represent the 10/2=5 th and 10/2+1=6 th values in the dataset. To find the median, we average them together to get The median salary is $49,000 per employee per year. The median is clearly a more viable measure. The mean takes into account all values, including the outlier, or “extreme” salary of $1.1 million per year. The median is not influenced by extreme outliers. To find the mean and median salaries in Excel we use the functions average() and median(). The parameter for both functions is the cell range corresponding to the dataset. Statistics for Decision-Making in Business © Milos Podmanik Page 58
2.3.2 Percentile Another useful tool for describing the location of data points is a percentile. Percentile The th percentile is a value such that percent of the values in a dataset (of values) are less than or equal to this value. To find the location of this value, that is, the index, , first arrange the data in ascending order. The index can be calculated by: . / That is, find the th percent of the number of observations. Round up if the index is a decimal and take the average of the values in positions and if the calculated value of is an integer. One of these two actions will be taken Example 2: Find the 50 th percentile for the salaries in Example 1:. Interpret the real-world meaning of this value. The values, in ascending order, are: We take . Since this is an integer, we average together the values in positions 5 and 6, giving us a value of 49. This means that 50% of employees represented in this dataset make $49,000 or less. Statistics for Decision-Making in Business © Milos Podmanik Page 59
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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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Page 21 and 22: 1.3Statistics in Excel When conduct
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Page 81 and 82: Chapter 3 Probability and Decision
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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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1 st Bushel 2 nd Bushel U1 U1 U2 U2
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Which, in its final state gives: Th
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Combination - Order Does NOT Matter
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( ) There is only a .9% chance that
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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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We can easily find that the probabi
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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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1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
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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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3) We cannot use this sample to cal
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Thus, we need to find the lower and
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We see that the standard deviation
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√ The lower limit is: √ And the
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following data was collected on the
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{ So, we have a set of twenty 1‟s
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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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Example 3: Many older homes have el
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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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el freq Nitrous Oxide (thous. Tons)
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Probability Pizza Size Distribution
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2. a. The long-run proportion of al
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6. This is the probability that we
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