PSYC1010 Unit 2: Descriptive Statistics
Frequency Distributions
Frequency
Counting the number of times, a score occurs
Symbol
o f
Distribution
Any organized set of data (scores)
Is there any unique order or pattern to the scores?
N = total number of scores
4 Ways to Organize Data
1. Simple Frequency
2. Relative Frequency
3. Cumulative Frequency
4. Percentile
Conditions for Frequency Distributions
Exhaustive
o There must be enough categories so that all observations fall into a category
Mutually Exclusive
o The categories must be distinct so that an observation will into only one category
Nominal/Ordinal Variables
Simply counting number of occurrences in each category
(DV is Sex)
Simple Frequency Distribution
Interval/Ratio Variables
Counting how many times a particular score occurs
To determine:
o How many categories to create
o How wide categories should be
Rules for making a frequency table
o Make score column and then, make a
frequency column
Raw Scores
Frequency Table
o Order scores from high to low
, Graphing
o Bar Graph
o Used for nominal or ordinal data
Bars do not touch each other
o Histogram
o This is a bar graph where the bars touch each other
o Used for a small number of scores
o Indicates there are no gaps in the X variable
o Used for interval or ratio data
o Ogive Curve
Efficient way to determine percentiles
Polygon
o Use with a large number of interval or ratio scores
o Continuous variable
Relative Frequency
o The proportion of N that is made up by a score’s simple frequency
o Fraction of the total N
o rel.f = f / N
o Grouping relative frequency distribution
o Same rule as simple frequency
o Cumulative Frequency
o The frequency of all scores
at or below a particular score
o Percentile
o The percent of all scores in the data
at or below a particular score
o percentile = [cf / N] x 100%
Grouped Frequency Distribution
Method to describe large data sets
Need to balance between too much or too little information
Guidelines
How many intervals?
Interval width? Simple value
The bottom score in each class interval should be a multiple of the width
All intervals should be the same width
Example
o 2015 NBA player salaries
Central Tendency
Calculating “…one number that summarizes everyone’s score”
Indication of the “location” of one person’s score relative to the sample (or population)
Measure of Central Tendency
o “…is a score that summarizes the location of a distribution on a variable”
Frequency Distributions
Frequency
Counting the number of times, a score occurs
Symbol
o f
Distribution
Any organized set of data (scores)
Is there any unique order or pattern to the scores?
N = total number of scores
4 Ways to Organize Data
1. Simple Frequency
2. Relative Frequency
3. Cumulative Frequency
4. Percentile
Conditions for Frequency Distributions
Exhaustive
o There must be enough categories so that all observations fall into a category
Mutually Exclusive
o The categories must be distinct so that an observation will into only one category
Nominal/Ordinal Variables
Simply counting number of occurrences in each category
(DV is Sex)
Simple Frequency Distribution
Interval/Ratio Variables
Counting how many times a particular score occurs
To determine:
o How many categories to create
o How wide categories should be
Rules for making a frequency table
o Make score column and then, make a
frequency column
Raw Scores
Frequency Table
o Order scores from high to low
, Graphing
o Bar Graph
o Used for nominal or ordinal data
Bars do not touch each other
o Histogram
o This is a bar graph where the bars touch each other
o Used for a small number of scores
o Indicates there are no gaps in the X variable
o Used for interval or ratio data
o Ogive Curve
Efficient way to determine percentiles
Polygon
o Use with a large number of interval or ratio scores
o Continuous variable
Relative Frequency
o The proportion of N that is made up by a score’s simple frequency
o Fraction of the total N
o rel.f = f / N
o Grouping relative frequency distribution
o Same rule as simple frequency
o Cumulative Frequency
o The frequency of all scores
at or below a particular score
o Percentile
o The percent of all scores in the data
at or below a particular score
o percentile = [cf / N] x 100%
Grouped Frequency Distribution
Method to describe large data sets
Need to balance between too much or too little information
Guidelines
How many intervals?
Interval width? Simple value
The bottom score in each class interval should be a multiple of the width
All intervals should be the same width
Example
o 2015 NBA player salaries
Central Tendency
Calculating “…one number that summarizes everyone’s score”
Indication of the “location” of one person’s score relative to the sample (or population)
Measure of Central Tendency
o “…is a score that summarizes the location of a distribution on a variable”
