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Unformatted text preview: ample standard deviation
s= ∑ ( ̅) = 156/4= 6.2 Heights of the players vary from the mean of 75 inches by 6.2 inches Variation and Standard Deviation – the more variation there is in a data set, the larger is the
Computing Formula for a Sample Standard Deviation (alternative formula)
= ∑ ∑ ⁄ = Three Standard Deviations Rule – almost all the observations of any data set lie within three
standard deviations to either side of the mean 3 Chebychev’s rule – 89% lie within three standard deviations on either side of the mean
Empirical Rule – if distribution of the data set is bell shaped, then 99.7% of the observations lie
within three standard deviations to either side of the mean.
3.3 The Five-Number Summary: Quartiles and Boxplots (invented by Tukey)
Percentiles – divide data set into hundreths
Deciles – divide data set into tenths
Quintiles - divide data set into fifths
Quartiles – divide the data into fourths = First Quartile Q1, = 25 median below the actual data
median; Second Q2, = middle, median; Third 50% Q3 = 75% median above the actual data
median, Q4 = 100%
Quartiles for Distributions: Uniform; Bell Shaped; Right Skewed (tail to right); Left...
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- Spring '14