Chapter 3 - Describing the middle and spread of data

Measures of central tendency

A single number that identifies the center of a data distribution

There are three measures of central tendency:

• WHAT

• WHAT

• WHAT 

There are three measures of central tendency:

• Mean

• Median

• Mode 

Mean

the average response 

Mode

the most common response

Median

middle response

Formulas to calculate mean

• M = (sum of X) / n 

• M = refers exclusively to the mean 

• X = collection of numerical data points of the variables 

• n = Number of data points in a sample 

Use mean instead of average because average could mean the most WHAT or WHAT version of a thing

Use mean instead of average because average could mean the most COMMON or TYPICAL version of a thing

Mode is good for summarizing WHAT data

Mode is good for summarizing NOMINAL data

A dataset can be WHAT if there are two very WHAT responses

A dataset can be BIMODAL if there are two very COMMON responses

Any data that isn’t numeric, the WHAT is the best measure to summarize data

Any data that isn’t numeric, the MODE is the best measure to summarize data

Use mode to describe WHAT data

Use mode to describe NOMINAL data

Use the mean or the median to describe WHAT or WHAT data

Use the mean or the median to describe INTERVAL or RATIO data

Outlier

rogue data points

When concerned about outliers, use WHAT as it isn't influenced by WHAT but the WHAT is, or show both.

When concerned about outliers use MEDIAN as it isn't influenced by OUTLIERS but the MEAN is, or show both.

Mode is not affected by WHAT 

Mode is not affected by OUTLIERS 

When the mean median and mode are similar the dataset has a WHAT distribution 

When the mean median and mode are similar the dataset has a SYMMETRICAL distribution 

Variability

Your data’s shape, distribution or shape

Range

Variability that indicates the distance the highest and lowest scores for your variable 

Range equation

Range = Largest value for a variable - lowest value for a variable 

Range creates a broad definition of WHAT - causes some problems since you don’t use all the WHAT 

Range creates a broad definition of VARIABILITY - causes some problems since you don’t use all the DATA 

Standard deviation

the typical distance of how far data points tend to be from the mean 

Variance is the standard deviation WHAT 

Variance is the standard deviation SQUARED 

Standard deviation is the WHAT of variance 

Standard deviation is the SQUARE ROOT of variance 

Using SPSS to Find Measures of Central Tendency and Variability 

1. Go to WHAT in the main menu and select WHAT then select WHAT 

2. Drag and drop your variable into the WHAT

3. Unclick WHAT table box 

4. Click on the WHAT button and make sure the boxes next to Mean, Median, Std. deviation, variance and range are selected 

Using SPSS to Find Measures of Central Tendency and Variability 

1. Go to ANALYZE in the main menu and select DESCRIPTIVE STATISTICS then select FREQUENCIES 

2. Drag and drop your variable into the VARIABLE PANE

3. Unclick DISPLAY FREQUENCY table box 

4. Click on the STATISTICS button and make sure the boxes next to Mean, Median, Std. deviation, variance and range are selected 

APA Mini Report for Measures of Central Tendency and Variability

1. WHAT and WHAT the heading 

2. Format your report so it's easy to read = WHAT-point font, WHAT the first line of each paragraph

3. Round your numbers to the WHAT decimal point, even if they are whole numbers 

4. Avoid WHAT voice 

5. WHAT English letters as abbreviations for statistics (Example, M for mean or SD for standard deviation) 

APA Mini Report for Measures of Central Tendency and Variability

1. CENTER and BOLDFACE the heading 

2. Format your report so it's easy to read = 12-point font, INDENT the first line of each paragraph

3. Round your numbers to the SECOND decimal point, even if they are whole numbers 

4. Avoid PASSIVE voice 

5. ITALICIZE English letters as abbreviations for statistics (Example, M for mean or SD for standard deviation) 

Method: WHAT

Method: Researchers collected (your variable) (Describe from who and how many studied) (M = WHAT, SD=WHAT)