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.