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Not surprisingly, the 50 th percentile is actually the median of the dataset! This is always true. In Excel, we can use the Percentile() function. The set-up of this function‟s parameters is: =percentile(cell range, p/100) Thus, for this dataset, we would have: 2.3.3 Quartiles Often times, data analysts like to think about data in terms of quartiles, or quarters. There are 4 quartiles and can be represented as follows: Quartile 1 = 25 th Percentile Quartile 2 = 50 th Percentile Quartile 3 = 75 th Percentile Quartile 4 = 100 th Percentile Statistics for Decision-Making in Business © Milos Podmanik Page 60
2.3.4 Rank What if, on the other hand, an employee wants to know what the rank of his salary is (he knows his percentile value) This requires reverse-engineering of the idea of a percentile. Without the use of any mathematical formulas, we would need to count the number of values that are equal to or lesser than salary in question. To make this easier, we can use Excel‟s Rank() function. The parameters we will use are as follows: = rank(value, cell range, 1) This will return the number of values that are less than or equal to the value in question. If we changed the parameter of 1 to a 0, Excel would return the ranking of that value, treating rankings as being similar to the ranks of, say, runners in a race. We will then need to divide this output by the number of observations in the dataset. To make the counting process more automated, we can take this output and divide it by the output of the count() function. This function will simply count the number of entries in the specified range, and has the following parameter: = count(cell range) Let‟s say the employee making $24,000 would like to know his salary‟s rank. To calculate, we would type the following: Giving us: Statistics for Decision-Making in Business © Milos Podmanik Page 61
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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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which has undergone no additional r
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Page 15 and 16: For the present time, we‟ll proce
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Page 19 and 20: (SOURCE: Essentials of Modern Busin
Page 21 and 22: 1.3Statistics in Excel When conduct
Page 23 and 24: We can make it a bit more presentab
Page 25 and 26: For measures such as the range, Exc
Page 27 and 28: We get: We can do the same for Old.
Page 29 and 30: Chapter 2 Visual Representations of
Page 31 and 32: We now have to enter a formula for
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Page 35 and 36: Alternatively, it is possible to in
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Page 39 and 40: Selected the copied graph. In Chart
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Page 45 and 46: You can either choose to have Excel
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Page 49 and 50: Select PivotChart and select the fi
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Page 53 and 54: Relative Frequency Histogram of Cal
Page 55 and 56: a. Using Excel, find the mean and r
Page 57 and 58: ̅ ̅ account for this discrepancy,
Page 59: 2.3.2 Percentile Another useful too
Page 63 and 64: Check the “Analysis ToolPak” an
Page 65 and 66: You‟ll immediately notice that a
Page 67 and 68: ̅ 2.4 Descriptive Statistics - Var
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Page 71 and 72: This gives us a nice measure of how
Page 73 and 74: We can immediately see the mean and
Page 75 and 76: Lastly, a normal curve is the most
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Page 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
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Page 89 and 90: 3.2 Joint Probability In the previo
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Page 93 and 94: There is less than a 1% chance that
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Page 97 and 98: sequence, one ball is chose at rand
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We could just as well have written,
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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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e. ( ) f. ; the average response ti
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2. a. The long-run proportion of al
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e. 20% of all children are expected
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e. The middle 50% score between abo
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5. b. This might indicate that the
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̅ We have that ̅ and √ . So our
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6. This is the probability that we
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