Understanding Percentiles, Quartiles, and Descriptive Statistics

Explore the concepts of percentiles, quartiles, and descriptive statistics explained by Ardavan Asef-Vaziri. Learn how percentiles indicate a variable's position and quartiles divide data into quarters. Discover how to calculate percentiles and interpret quartiles in statistical analysis. Dive into the interquartile range and its importance in data analysis.

• Percentiles
• Quartiles
• Descriptive Statistics
• Statistical Analysis
• Ardavan Asef-Vaziri

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1. Percentile Quartile Ardavan Asef-Vaziri

2. Rank, Percentile, and Quartile Rank. Where a variable stands compared to all the variables in the data set. Median. At least 50% of observations are less than or equal to median, and at least 50% of observations are greater than or equal to median. Median is 50th percentile. Percentiles. Xth percentile =R means at least X% of observations are less than or equal R, and at least 100-X% of observations are greater than or equal R. The 20th percentile for the grades of students in SOM307 is the score where at least 20% of the grades are less than or equal to this number. In the set of the following 8 numbers, 125, 180, 180, 180, 200, 200,180, 200, 220, the 25th percentile is 180. Given N as the number of observations Location of PERCENTRANK.EXC p(N+1)=pN+p Location of PERCENTRANK.INC p(N-1)+1=pN+(1-p) PERCENTRANK.INC is from 0 to 1 PERCENTRANK.EXC is from 1/N to 1-1/N 2 Descriptive Statistics, Ardavan Asef-Vaziri.

3. Percentile A 100th percentile in PERCENTILE.INC means at least 100% greater than or equal to a specific value and at least 0% less than or equal to that value. This is not possible. The same is true for 0th percentile. That is why 0th and 100th percentiles are not defined in PERCENTILE.EXC Percentile and Rank are also available in Data Analysis ToolPack, but we prefer Excel functions 3 Descriptive Statistics, Ardavan Asef-Vaziri.

4. Quartile Quartile is the same as Percentile, but it is only defined for 0%, 25%, 50%, 75%, and 100% It is defined as 0st, 1st, 2nd, 3rd, 4th quartile. Kth Quartiles where K=1,2,3,4, means K portion of observations are greater than or equal to this number, and (4-k)/4 portion of observations are less than or equal to this number. QUARTILE.INC() is defined for 0,1, 2, 3, 4. QUARTILE.EXC() is not defined for 0 and 4 If it is not specified INC or EXC, then use EXC. 4 Descriptive Statistics, Ardavan Asef-Vaziri.

5. Percentile & Quartile https://youtu.be/eMa1YN-zKMQ (15 mins.) 5 Descriptive Statistics, Ardavan Asef-Vaziri.

6. Percentile & Quartile (15 mins.) A is computed as 80 =PERCENTILE.EXC($B$3:$B$102,M1/100) 80 =PERCENTILE.INC($B$3:$B$102,M1/100) That means at least 60% of the data is less than or equal to 80, and at least 40% of data is greater than or equal to 80 60 percentile of the blue data set in column D Grade Grade 79 59 90 59 84 90 70 64 82 80 60 72 82 66 90 89 89 88 58 75 67 67 63 77 74 61 85 73 88 85 56 87 86 81 76 80 90 80 75 63 77 85 68 89 Percentile % Quartile =PERCENTILE.EXC =PERCENTILE.INC pN+p Quartile Excluded Quartile Included pN+(1-p) 95 87.1 85.2 84.25 83 80 74 70.6 66 63.75 63 60 52 1 0.9 0.8 0.75 0.7 0.6 0.5 0.4 0.3 0.25 0.2 0.1 0 4 95 87.9 85.8 84.75 83 80 74 70.4 66 63.25 63 60 3 84.75 84.25 2 74 74 1 63.25 63.75 0 52 IQR IQR 21.5 20.5 Recorded Lecture Inter Quartile Range https://youtu.be/eMa1YN-zKMQ 6 Descriptive Statistics, Ardavan Asef-Vaziri.

7. z-Score- Standard Normal Variable What is standard Normal Variable. What does it mean? What is z-Score? Suppose I ask each of the students in this class- how much do you have in your checking account? Suppose one student tells me $600. That is x=$600 This number does not have that much meaning. But if I know the average of class, and suppose it is $600. That is ?=500. Now x- ? tells me some thing. x- ? = 500-600=-100. It tells me you have below an average student. That is a good piece f information. However, If I compute the standard deviation of class and if that is =$80, I can compute z= (x- )/ = (600-500)/80=1.25 Not I know (i) you have more than average, and 1.25 standard deviation above the average. That is what z means. 7 Descriptive Statistics, Ardavan Asef-Vaziri.

8. Percentile & Quartile https://youtu.be/eMa1YN-zKMQ (13 mins) 8 Descriptive Statistics, Ardavan Asef-Vaziri.

9. Percentile & Quartile No matter what distribution, at least 1-1/k2 of observation is between ? ??. 0.8 This Lecture is recorded at https://youtu.be/0qxtq66CbYw x values 7076 3295 4147 5932 5368 3650 6097 Mean= Above or below Mean 2337.743 1926.743 -202.257 1532.743 -1347.26 2130.743 367.7429 -126.257 797.7429 -2061.26 -1443.26 3283.743 3187.743 752.7429 3269.743 1353.743 394.7429 -1060.26 -3359.26 -6402.26 -591.257 2970.743 -1496.26 -3122.26 1208.743 -223.257 1300.743 -1473.26 -228.257 -45.2571 1193.743 -2335.26 -1058.26 3566.743 188.7429 2038.743 -902.257 638.7429 -712.257 -3091.26 629.7429 1855.743 -1255.26 1715.743 -1348.26 920.7429 -3220.26 1933.743 -684.257 527.7429 -1088.26 491.7429 -2639.26 -59.2571 4015.743 292.7429 2165.743 -3046.26 2037.743 -881.257 Count>0 1358.743 556.7429 -3948.26 219.7429 406.7429 734.7429 -2359.26 -1311.26 -2390.26 1205.743 6665 8022 7709 2403 6594 5230 5295 4738.26 StdDev= 2006.35 4536 7926 3242 3680 3483 2099 790 6271 5491 1616 8305 6454 4679 4958 3391 8008 5947 4927 3390 8754 5145 6869 6092 4515 6777 5659 5031 5473 5106 5133 6039 3836 1518 6904 2379 4612 3678 3265 5377 6672 1692 3427 5536 1379 4510 4026 4054 6776 2348 2677 -1664 4693 1647 5266 3857 5944 0.9 0.7 0.6 1-1/(k^2) 0.5 0.4 0.3 0.2 %>0 0.1 37 0.528571 0 1 1.5 2 2.5 3 How Many StdDev Above or Below Mean 1.17 0.96 -0.72 1.64 -0.29 1.48 0.59 -1.16 0.31 0.92 -0.54 0.25 0.68 0.28 Mean= 0.00 StdDev= What % in a Specific Range 0 1 1 0 1 0 1 0 1 1 1 1 1 1 k -0.10 1.59 -0.75 -0.53 -0.63 -1.32 -1.97 0.76 0.38 -1.56 1.78 0.86 -0.03 0.11 1.00 -0.67 1.63 0.60 0.09 -0.67 2.00 0.20 1.06 0.67 -0.11 1.02 0.46 0.15 0.37 0.18 0.20 0.65 -0.45 -1.61 1.08 -1.18 -0.06 -0.53 -0.73 0.32 0.96 -1.52 -0.65 0.40 -1.67 -0.11 -0.36 -0.34 1.02 -1.19 -1.03 -3.19 -0.02 -1.54 0.26 -0.44 0.60 Numbers that fall out of ? 3? are outliers 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1.1 0.74286 9 Descriptive Statistics, Ardavan Asef-Vaziri.