STAT 2300 3.4-.5

measures of position

measures of position

Measures that determine the position of a single value in relation to other values in a data set. Quartiles, percentiles, and percentile rank are examples of measures of position.

z-scores

measure the distance of a score from the mean in units of standard deviation

positive

if the data value is larger than the mean it is a _____ z-score

negative

if the data value is smaller than the mean it is a _____ z-score

Percintile

breaks observation into 100 parts

Z = (X - μ) / σ

z score formula

-1 and 1

68%

-2 and 2

95%

-3 and 3

99.7%

quartiles

Values that divide a data set into four equal parts

first quartile

25th percentile

second quartile

the median of the entire data set

third quartile

the median of the upper half of the data set

Interquartile Range (IQR)

Q3-Q1, the middle 50% of the data, resistant

Q1-1.5(IQR)

lower fence

Q3 + 1.5(IQR)

upper fence

median and IQR

are better measures of center and spread for skewed distributions.

mean and standard deviation

are better measures of center and spread for relatively symmetric distributions.

five number summary

minimum, Q1, median, Q3, maximum

Boxplot

A graph of the five-number summary., number line, box from lower quartile Q1 to upper quartile Q3, line at median, line to smallest and largest (not outliers)

whiskers

Lines from the min to Q1 and from Q3 to the max

outliers

are marked w asterisk