Psyc202 Chapter 2 – Frequency Distributions Sept. 11
2.1 Introduction to Frequency Distributions
Frequency Distribution: an organized tabulation of the number of individuals
located in each category on the scale of measurement
Takes disorganized scores and organizes them from highest to lowest, grouping
together all individuals who have the same score
Presents a picture of how the individual scores are distributed
2.2 Frequency Distribution Tables
List different X values in a column from highest to lowest. Beside each X value,
we indicate the number of times that particular measurement occurred in the data
Nominal scale values can be ordered in any order. All other 3 scales must be
ordered highest to lowest.
By adding up frequencies, you can find out the total number of scores
Σf = N
Obtaining ΣX From a Frequency Distribution Table:
Add X values as many times as they appear in the frequency column.
Alternatively, multiply Xvalue by frequency to get fx. Add all fx values to
Proportions and Percentages:
Proportion or ‘Relative Frequency’: measures the fraction of the total
group associated with each score. Ex. If 2 our of 10 people got a score of
4 the proportion would be 2/10 or 0.20.
Proportion describes frequency (f) in relation to the total number (N).
Grouped Frequency Distribution Tables:
Class Intervals: groups of scores rather than individual values.
Example: listing frequency of scores in the 90s and 80s versus listing
individually 99, 98, 87, 85, etc.
Rules of Intervals:
1. Grouped frequency distribution table should have about 10
2. Width of each interval should be a relatively simple number. Ex.
Counting down by 5s or 10s.
3. Bottom score in each class interval should be a multiple of the
width. Ex. If counting down by 10s last # should be 10
4. All intervals should be the same width
Generally, the wider class intervals are, the more specific information is
Real Limits and Frequency Distributions:
Note that real limits apply to frequency distribution tables. Example:
interval of 9094 actually has a lower limit of 89.5 and an upper limit of
94.5. 9094 are apparent limits not real limits. Note: the width of the interval must be the distance between the 2 real
limits. Ex. If interval goes up by 5 points then lower interval goes down by
5 points (89.5 and 94.5)
2.3 Frequency Distribution Graphs
General rule for graphs: height (Yaxis) should be 2/3 – ¾ length of the xaxis
(so Xaxis should always be longer)
Graphs for Interval or Ratio Data:
If data from interval or ratio scale, 2 options:
Histograms: bar graph (remember that the width of bars must
reach real limits). No spaces between bars. If grouping scores,
make sure bar width includes all scores in group as well as real
limits (figure 2.3 page 45).
Modified Histogram: more basic and less accurate, but
frequency is shown by number of blocks rather than yaxis
Polygons: a graph with dots connected by lines (not of best fit).
Starts at 0 and ends at 0. (p. 46). If using intervals, position dot in
middle of interval (find mean of interval).
Graphs for Nominal or Ordinal Data:
Bar Graphs: same as histograms but with spaces between bars
Graphs for Population Distributions:
When dealing w