Stats 2.3: Measures of Central Tendency

Mean, Median, Mode

measure of central tendency

value that represents a typical, or CENTRAl entry of a data set

Mean, Median, Mode

mean

sum of data entries divided by number of entries

• population mean = µ

• sample mean = x̄

Mean, Median, Mode

median

value that lies in the MIDDLE of the data when the data set is ordered

• ODD number of entries → median = middle most #

• EVEN number of entries → median = mean of 2 middle entries

Mean, Median, Mode

mode

data entry that occurs with GREATEST FREQUENCY

• may have multiple or no modes

Mean, Median, Mode

bimodal

data set that has 2 modes

Mean, Median, Mode

outlier

data entry far removed from the other entries in the data set

Weighted Mean & Median

weighted mean

mean of data sets where entries w/ varying weights

• weighted mean = [sum of (weight × entries)] / [sum of weights]

Weighted Mean & Median

mean of frequency distribution

mean of frequency distribution = [sum of (midpoint × frequency)] / sample size

Weighted Mean & Median

Guidelines: Finding Mean in Grouped Data

1. find MIDPOINT of each class

2. find SUM of (midpoint × frequencies)

3. find SUM of frequencies

4. find mean of frequency distribution

Shape of Distributions

symmetric

vertical line can be drawn through middle of the graph → halves are approximately mirror images

• mean = median (approximately)

Shape of Distributions

uniform (aka rectangular)

all entries/classes have (approximately) equal frequencies

• symmetric by default definition

Shape of Distributions

skewed

“tail” of grpah elongates more to one side than another

• skewed left = tail extends to left

  • mean < median

• skewed right = tail extend to right

  • mean > median