Frequency Distributions
Interval
range of numbers that in between numbers called lower and upper boundaries
Usually ___ to ___ intervals
5 to 15
A psychologist wants to know how many of her clients continue with therapy for at least 12 days. ◦ If she constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer her question? ‣ A. cumulative frequency distribution ‣ B. cumulative percent distribution ‣ C. a simple frequency distribution ‣ D. A relative percent distribution
A. cumulative frequency distribution
A psychologist wants to know the percentage of her clients continue with therapy for at least 12 days. If she constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer her question? ‣ A. a cumulative frequency distribution ‣ B. a cumulative percent distribution ‣ C. a simple frequency distribution ‣ D. A relative percent distribution
B. a cumulative percent distribution
A researcher reports that 12 persons in a sample of 60 reporters getting between 4 and 6 hours of sleep per night. What is the relative percentage for this interval? ‣ A. 24% ‣ B. 22% ‣ C. 20%
C. 20% ‣ 20% = 12/60 x 100
A researcher wants to determine how many participants will take less than 24 seconds to complete a cognitive performance task. If he constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer his question? * A. Simple Frequency Distribution * B. Cumulative Frequency Distribution
Cumulative Frequency Distribution
What is the second step of determining intervals?
Determine the interval width (width = real range/number of intervals)
What is the first step of determining intervals?
Find the real range (Real Range = largest # - smallest # + 1)
Key words for Top-down cumulative frequency:
Greater than / at or above /at least
Key words for Bottom-up cumulative frequency:
Less than / at or below / at most
What is the third step of determining intervals?
List the boundaries of each interval, beginning with the lowest interval
What is the problem with too many intervals?
Many values have zero frequency and unclear shape of distribution
In comparison to a frequency table, a histogram...
Provides a direct view of frequency distribution
What is the real range?
Real Range = largest # - smallest # + 1
Formula for Relative Percent Distribution
Relative Percent Distribution = observed freq./total freq. x 100%
A researcher wants to determine how many participants will take less than 24 seconds to complete a cognitive performance task. If he already has a simple frequency table for these data, with largest values on the top, and smallest value at the bottom, what type of cumulative distribution does he need to appropriately answer the question? ‣ A. Simple Frequency Distribution from the Bottom Up ‣ B. Cumulative Frequency Distribution front the Top Down
Simple Frequency Distribution from the Bottom Up
What are the two ways of displaying a frequency table?
Using tally marks into frequencies; histograms
categorical variables
Variables that only have categories
tally marks
Vertical lines and backslash that represent the data.
Pie Chart
a graphical display in the shape of a circle that is used to summarize the relative percent of discrete and categorical data in sectors; summarize qualitative and discrete data
Round up when....
above .5
Round down when
below .5
An example of categorical variable
ethnicity, marital status
histograms
graphs that distribute intervals along horizontal scales (x-axis) and list frequency of scores on each interval on vertical scales (y-axis); for continuous variables
An example of a discrete variable
number of siblings, number of traffic accidents
A cumulative percent is also called a ______________.
percentile rank
What is the problem with too little intervals?
scores in an interval are the same; more info is lost
Cumulative Frequency
sum of frequencies across a series of intervals
Cumulative percent distribution
sum of relative percents across a series of intervals
Simple Frequency Distribution
summarizes how often scores occur in a data set
Bar Chart
summarizes the frequency (or percent) of data in whole units or categories; for discrete variables
Relative Percent Distribution
the percentage from 0% to 100% that describes the portion of data in each interval
Discrete Variables
variables that can only take on specific values; no other values can exist between these numbers.