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Z-Scores and Percentiles

by: Andrew Isbell

Z-Scores and Percentiles MAT 120

Marketplace > Tri-County Technical College > Mathmatics > MAT 120 > Z Scores and Percentiles
Andrew Isbell

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About this Document

These notes cover what z-scores are and how to calculate percentiles from a data set as well as why this information is beneficial in a statistics setting
Probability and Statistics
Merle Glick
Class Notes
Mathematics, Probability, Statistics
25 ?




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This 2 page Class Notes was uploaded by Andrew Isbell on Thursday September 1, 2016. The Class Notes belongs to MAT 120 at Tri-County Technical College taught by Merle Glick in Fall 2016. Since its upload, it has received 3 views. For similar materials see Probability and Statistics in Mathmatics at Tri-County Technical College.


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Date Created: 09/01/16
Z­scores and Percentiles  Andrew Isbell  ­Population z­score  Z­ x­ Pop. Mean/ Standard deviations  ­Sample z­score Z­x­Sample Mean/ Standard deviations Z­scores give an approximation of the averageness of a value compared to the population as a whole.  Interpret Percentiles  ­The kth percentile which means that the kth amount did less/worse than you  Quartiles  ­The first quartile, denoted Q1, divides the bottom 25 percent of data from the top 75. This is the 25   th percentile  ­The second quartile (same as the median) divides the bottom 50% of data from the top 50% of data. This  th is the 50  percentile. ­The 3  quartile divides the bottom 75% of data from the top 25%. This is the 75  percentile. ­Minimum to Q1 to Q2 (Median) to Q3 to Maximum ­Order of data from least to greatest rd ­The Interquartile Range, IQR is the difference between the 3  quartile and the first quartile (Q3­Q1) ­One benefit of IQR is that it isn’t effected by outliers nearly as much as the Range is, so it makes the data set resistant, which makes for much more reliable results.  ­Mean and Median are measures of the center of a data set and Standard Deviation and IQR are measures  of the spread of a data set.  ­Median and IQR are resistant to an outlier(s) in any statistical case. Which should I Use?  ­Symmetric shape distribution – mean is best measure of central tendency & standard deviation is best  measure of dispersion.  ­Skewed left or right­ median is the best measure of central tendency & IQR is best measure of  dispersion.  Checking for outliers by using Quartiles  Step 1: Determine Q1 and Q3 Step 2: Find IQR  Step 3: Determine fences (cutoff points for outliers) Lower fence = Q1 ­1.5(IQR) Higher fence= Q3+1.5(IQR)  ­Any values below lower fence or above higher fence is deemed an outlier and should be ignored  for the most part and especially when drawing conclusions. 


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