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Elementary Statistics

by: Morgan Walker

Elementary Statistics Stat 2013

Morgan Walker
OK State
GPA 3.2

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Week 3 chapter 3
Elementary Statistics
Robert Adam Molnar
Class Notes
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This 3 page Class Notes was uploaded by Morgan Walker on Saturday January 30, 2016. The Class Notes belongs to Stat 2013 at Oklahoma State University taught by Robert Adam Molnar in Winter 2016. Since its upload, it has received 20 views. For similar materials see Elementary Statistics in Statistics at Oklahoma State University.


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Date Created: 01/30/16
Chapter 3 Data Description Numbers are used to describe/ summarize data Average- the center values of distribution Measure of central tendency- measure of average Measure of variation-summarizes the spread of distribution Measure of position- describes where data falls in an ordered set Nominal mean- sum of numbers in a set divided by the amount of numbers present in the set, average of all the numbers  Strength- unique, can be found easily  Weakness- not good for nominal/ ordinal, not exact, easily contaminated, sensitive to extreme values Weighted mean- used for continuous data where each value has a weight  Ex: Grade percentage Median- the middle number  Strength- more robust than mean; single value change or outlier has less effect, better than mean for nonsymmetrical distributions  Weakness- harder to compute because you have to put the values in order, not for nominal variables, cannot combine two sets without knowing all values Mode- the value that shows up more than once or shows up the most  Strength- used for nominal/ ordinal data, no order just counting  Weakness- 2 or more can exist Midrange- average of lower and higher number in a set  Strength- unique less computation than mean  Weakness- not good for nominal and ordinal, limited ordering, easily contaminated and sensitive to extreme values Measure of variation- dispersion of data is more important than central measure Variance- best mathematical properties Deviation- the difference from mean Standard deviation- square root of variance “typical” Sample variance- Degrees of freedom (d.f)- the number of “free” observations  Data sets starts with n d.f and loses one degree of freedom for each calculated statistic o Starts with a certain amount of unknown numbers and for each number found the amount of unknown goes down  After estimating the sample mean before computing sample variance, the data set has (n-1) d.f left Coefficient of Variation- used to compare deviations between groups  Standard deviation divided by mean o Expressed as a percentage Empirical Rule- MUST BE BELL SHAPED GRAPH  68% will fall within one standard deviation  95% will fall within two standard deviations  99.7% will fall within three standard deviations Measures of Positions  Mean, midrange, variance and other measures have units  Percentiles will not have units o Dividing the data into 100 groups o Always round down, cannot go over  Deciles- 10, 20, 30 o The third decile is the 30  Quartile- four equal size groups o Can be percentiles, but are often computed with multiple medians o There are different computation rules but this one is more common  Q1 is the median of values less than median  Q2 is the median of all the values  Q3 is the median of values more than the median  For Q1 and Q3 DO NOT include the median observation in “less than” and “greater than” o Interquartile Range (IQR)- Q3-Q1 Outliers Observation that is suspected to be outside the typical pattern of distribution  Very high or very low Numeric test labels a point as the outlier if the point is  More than Q3 + 1.5*(IQR)  Less than Q1- 1.5*(IQR) Standard Scores Obtained by subtracting the mean and dividing by the standard deviation  160-100/ 20= 3 Exploratory Data Analysis (EDA) EDA- refers to everything in descriptive statistics (all of chapters 2 and 3) Five number summary for a variable contains 1. Minimum 2. Q1 3. Median (Q2) 4. Q3 5. Maximum Boxplot Unmodified boxplot consists of a box from Q1 to Q3 with a central line as the median then extensions to the minimum and maximum


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