# SPAN 101 Chapter Notes - Chapter 5: Squared Deviations From The Mean, Interquartile Range, Standard Deviation

by OC2168805

Department

SpanishCourse Code

SPAN 101Professor

Enrique ManchonChapter

5This

**preview**shows half of the first page. to view the full**1 pages of the document.**CH 5 DISPLAYING AND DESCRIBING QUANTITATIVE DATA

If the shape is skewed:

• report the median and IQR

• mean + standard deviation (mean and median differ)

If the shape is unimodal and symmetric:

• mean and standard devation

• possibly the median and IQR

• unimodal: IQR is usually a bit larger than the standard deviation

Median + IQR; mean + standard deviation

Boxplots

• Centre: a box that shows the middle half of the data

• Height of the box: IQR

• Upper fence = Q3 + 1.5 IQR

• Lower fence = Q1 – 1.5 IQR

• Whiskers: skewness

Average: ý = Total / n = Ey/n

Median: resistant to unusual observations or shape of the distribution

Arithmetic: non related values

Geometric: used for rates where each measurement depends on the previous one.

GM: √+R x +R x… x+Rn - 1

Harmonic: rates that are not dependent on each other

(M: n//y+/y+…/yn

Interquartile range (IQR): summarizes the spread by focusing on the middle half of

the data. Q3-Q1

Variance: average of the squared deviations

s2 = E(y-ý)2/ n-1

Standard deviation: measures of spread to have the same units as the data

s2 = √E(y-ý)2/ n-1

Standardized value or z score: how many standard deviations a value is from the

mean: z = y-ý/s

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