Chapter 2: Frequency Distributions in Tables and Graphs
Cumulative frequency distribution
Distributes sum of frequencies across a series of intervals
Cumulative relative frequency distribution
Distributes sum of relative frequencies across a series of intervals
A dot-line graph plotted at the midpoint of each interval
Frequency polygon
Bar chart/graph
Graphical display used to summarize frequency of discrete and categorical data, distributed in whole units or classes
Stem and leaf plot
Graphical display where each individual score is listed, organized by common digits shared by all scores listed to left, with remaining digits for each score listed to the right
Open interval
Interval with no defined upper or lower boundary
Cumulative relative frequencies sum to what?
1.0
The sum of relative frequencies across all intervals is equal to what?
1.0
What is a key distinction between a stem-leaf display and a histogram?
A stem-leaf display lists actual scores in a distribution vs. a histogram lists frequencies
Graphical displays similar to histograms, except that the vertical bars or rectangles do not touch
Bar charts
Cumulative frequencies can be added from the top down and...
Bottom up
Summary display that distributes the sum of frequencies across a series of intervals
Cumulative frequency distribution
Outliers
Extreme scores that fall substantially above or below most other scores in a distribution
True or False: a relative percent sums to total frequency count
False, a relative percent sums to 100%
A student scores in the 80th percentile on an exam, what does this mean in comparison to all other students?
The student scored higher than 80% of all others who took the same exam
When would a researcher construct a relative frequency table?
To summarize large data sets
True or False: a researcher observes that a single parent works 42.25 hours per week, the degree of accuracy of 42.25 is to the hundredths place (0.01)
True
Ogive
Dot-line graph summarizing cumulative percent of continuous data at upper boundary of each interval
Frequency polygon
Dot-line graph used summarizing frequency of continuous data at the midpoint of each interval
Rules for simple frequency distributions
Each interval is equidistant, the same score cannot occur in more than one interval, each interval is defined (it has a lower and upper boundary)
True or False: histograms are used to summarize ungrouped data, which is why each vertical rectangle touches the other
False, histograms are sued to summarize grouped data
A summary display for a distribution of data organized or summarized in terms of how often (or frequently) scores occur
Frequency distribution
Pie chart
Graphical display in shape of a circle, used to summarize relative percent of discrete and categorical data into sectors
Histogram
Graphical display summarizing frequency of continuous data, distributed in numeric intervals (grouped)
True or False: cumulative relative frequencies are added from top down or bottom up
True
True or False: whether you cumulate a frequency distribution from bottom up or top down depends on how you want to discuss the data
True
What are the data called when the frequency of each individual score or category is listed?
Ungrouped data
Percentile point
Value of an individual or score within a larger distribution
A dot-line graph plotted at the upper boundary of each interval
Ogive
Real range
One more than the difference between the largest and smallest value
Rules for constructing a histogram
(1) a vertical rectangle represents each interval and the height of the rectangle equals the frequency recorded for each interval, (2) each rectangle represents the frequency of all scores in a distribution, (3) each rectangle touches adjacent rectangles at the boundaries of each interval
What is the recommended number of intervals that should be included in a simple frequency distribution?
5-20 intervals
An ogive graphically summarizes what type of frequency distribution?
A cumulative percent distribution
Relative frequency distribution
Distributes proportion of scores in each interval, computed as frequency in each interval divided by total number of frequencies recorded
Cumulative percent distribution
Distributes sum of relative percents across series of intervals
Proportion
Part of all measured data, sum of all scores equals 1.0
Percentile rank
Percentage of scores with values that fall below a specified score in a distribution
Relative frequencies are commonly reported in academic journals as percents, why?
Percents are easier to read than decimals
Interval width
Range of values contained in each interval of a grouped frequency distribution
Grouped data
Set of scores distributed into intervals, frequency of each score can fall into any given interval
Ungrouped data
Set of scores or categories distributed individually
Simple frequency distribution
Summary display for (1) the frequency of each individual score or category (ungrouped data) or (2) frequency of scores falling within defined groups/intervals (grouped data) in a distribution
When is it appropriate to summarize frequencies for ungrouped data?
When data sets have only a few different scores and for qualitative or categorial variables
When cumulating frequencies from bottom up, you typically want to discuss the data in terms of?
"At most", "less than", and "at or below"
When cumulating frequencies from top down, you typically want to discuss data in terms of?
"At or above"
Interval
Discrete range of values within frequency of a subset of scores
Relative percent distribution
Distributes percentage of scores occurring in each interval relative to all scores distributed
Frequency distribution
Distribution of data organized or summarized in terms of how often a category, score, range of scores occurs
Why is it generally inappropriate to include an open interval in a simple frequency distribution?
It makes it difficult to identify if outliers exist in a data set
Frequency
Number of times/how often a category, score, or range of scores occurs
Interval boundaries
Upper and lower limits for each interval
