Descriptive Statistics CH 4 PDF

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Jolie Wormwood
Descriptive statistics...

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CHAPTER 4: DESCRIPTIVE STATSTICS MEASURES OF CENTRAL TENDENCY Descriptive statistics - Describe data o Data from your sample - Two main categories Measures of central tendency - Describe most typical or most common value of a variable in your data: - 3 measures of central tendency o Mean, median, and mode o Mode: reflects the most frequent value in a distribution  Ex: 5,2,6,5,7,8,2,5  Reorder data set smallest to largest o 5 is the mode  Bimodal or multimodal is when you have two modes  Pros:  easy to identify  Not as sensitive to extreme values  Cons:  Based on a singular value (not as representative of the entire data set)  Not always useful in comparing data sets o Median: reflects the middle value when observations are ordered from smallest to largest (or vice versa); a ‘balance point’, with an equal number of values above and below  Ex: 2,2,9,6,8,8,9,1,2,3,7,4  Order from smallest to largest  4+6=10/2=5  Pros:  Takes all values into account  Not sensitive to extreme values o 11,12,13,14,15  13 is the median o 11,12,13,14,20  13 is the median  Cons  Can be difficult to compute (by hand) with a large number of values  May not be an actual value in the data set (if even number of values)  May not be a very common value in the data set o Mean: mathematical average and most commonly used measure of central tendency  Obtained by  Adding up all the individual numbers for variable EX  Dividing by the sum of values by N  M=EX/N  Notation

CHAPTER 4: DESCRIPTIVE STATSTICS MEASURES OF CENTRAL TENDENCY

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N= mean or X bar X= individual score N= number of participants/observations Xi: subscripts indicate an individual score o X1= 1 participant X2= two participants  E=summation sign  The mean serves as the algebraic balance point if a distribution (the mathematical ‘middle’):  Whereas the median balances the number of values on either side, the mean balances the distances between the mean and values on either side  For a given variable, if you take the distance between each individual value for the mean, and you add them all up, the sum will always be 0 o Negative sum will equal positive sum  Pros:  All values are included in its calculation Cons:   Very sensitive to extreme values o Bell shaped distribution  Values of mean, median, and mode are close together o Bimodal (or polarized) distribution  Mean and median are not good ways to describe typical responses o Skewed distribution  Mean gets pulled towards larger numbers  If a frequency distribution is skewed the median, and one or more modes, may be better indicators of central tendency more than the mean Categorical data - Mean is never appropriate - Mode is always appropriate...