Frequency Distribution
Organization of data to show the number of times each score occurs in the sample
Ungrouped Frequency Distribution
1. List each individual score or category on the scale in order from lowest to highest or highest to lowest
2. For each score or category, indicate the frequency, or the number of times it occurs in the data set
Grouped Frequency Distribution
1. Scores or vales are grouped into intervals
2. For each interval, indicate the frequency or number of scores
Symmetrical
Each half of the distribution is the mirror image of the other half
Normal
Symmetrical, bell-shaped distribution
Skewed
Asymmetrical with a few extreme values on one side of the distribution
Positively Skewed
Many relatively low values and few extremely high values
Negatively Skewed
Many relatively high values, and few extremely low values
Bimodal
Having two distinct peaks
Kurtosis
Flatness or peakedness of the distribution
Platykurtic
Flat
Leptokurtic
Sharply peaked
N =
?f (sum of all the frequencies, total number of all the scores in the sample)
Proportion =
p = f / N
Percentage of Proportion =
(f / N) x 100
Cumulative Frequency
Sum of the frequencies at and below that category or value
Cumulative Percentage (c%) =
(cf / N) x 100
How many intervals you you usually want? And Equation
1. Usually want around 10 intervals
2. Interval width = (highest value - lowest value) / 10
Percentile and Percentile Rank
Both give information about cumulative percentage (c%)
Percentile
Usually refers to a score corresponding to a particular rank. Ex. For the ungrouped frequency distribution example, the score of 6 is at the 97th percentile.
Someone takes a standardized test and gets a score of 650. The score report shows that the percentile rank is 75. What does that mean?
Only 25% of people who took that test did better. Or. That person did better than 75% of everyone who took that test.
For graphing frequency distributions, the vertical axis (Y) is used...
To display frequency
For graphing frequency distributions, the horizontal axis (X), is used...
To display scores/categories of the variable
Bar Graph
For discrete data; vertical bar centered over each score or category on X axis; adjacent bars do not touch
Frequency Histogram
For continuous data; vertical bar centered over each score or score interval on X axis and bars touch
Frequency Polygon
For continuous data; point centered over each score or score interval on X axis and points are connected by strait lines