PSY201: Chapter 2 - Frequency Distributions Flashcards
Frequency Distributions basics
simplifying + organizing data
organized tabulation showing exactly how many individuals located in each category on scale of measurement
Frequency Distributions basics
presents an organized pic of entire set of scores
shows where each individual is located relative to others in distribution
Frequency Distributions Tables
2 columns - 1 listing categories (X) + 1 for frequency (f)
X column, values listed from highest to lowest, without skipping any
Frequency Distributions Tables
frequency column - tallies determined for frequencies for each X value
sum of frequencies should equal N
Frequency Distributions Tables
3rd column - proportion (p) for each category: p = f/N
sum of the p column = 1.00
4th column - % of distribution corresponding to each X - multiplying p by 100
sum of the % column = 100%.
5th column for cumulative percent
Regular Frequency Distribution
Summarizes sets of data that require little additional organization
data span relatively narrow range of values/categories
All raw data shown
Grouped Frequency Distribution
Used when set of scores covers wide range of values
Group data into intervals – ranges of values - to make easier to understand
Grouped Frequency Distribution
X column lists groups of scores - class intervals
Grouped Frequency Distribution Rules
- interval width selected so table has approx 10 class intervals
- Width simple number (2, 5, 10)
Grouped Frequency Distribution Rules
3. Bottom score in each class interval multiple of width width of 10, bottom score multiple of 10 4. Intervals should all have the same width & cover complete range scores
Grouped Frequency Distribution
Real Limits
Advantage of no ambiguity of class membership
No gaps
easily transformed into graphical representation (frequency histogram), directly from table
Frequency distribution graphs
Visual representation of frequencies
Useful because they show the entire set of scores
can determine highest score, lowest score, + where scores are centered
shows whether scores clustered together/scattered over wide range
Frequency distribution graphs
In most, X values listed on the X axis + frequencies listed on the Y axis
Frequency distribution graphs
X consist of numerical scores from interval/ratio scale ⇒ histogram/polygon
nominal/ordinal ⇒ bar graphs
Graphs for Interval/Ratio scales: Histograms
Bar centered above each score/class interval height of bar = frequency + width extends to real limits adjacent bars touch
Graphs for Interval/Ratio scales Polygons
dot centered above each score - height of dot = frequency
join dots with straight lines
additional line drawn at each end to bring graph back to zero frequency
Polygons
for plotting frequency of continuous variables
Communicates same info
shape of distribution emphasized
Can be superimposed on a histogram
Graphs for Nominal or Ordinal data: Bar graphs
X nominal/ordinal
gaps/spaces left betw adjacent bars
scale made up of distinct categories – not continuous/not necessarily same size
Pie charts
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Relative frequency
Many pops so large - impossible to know exact frequency
distributions can be shown using relative frequency instead
Smooth curve
scores in pop measured on interval/ratio scale ⇒ present distribution as smooth curve not a jagged polygon
emphasizes fact that distribution not showing exact frequency for each category
Shape
graph shows shape of distribution
symmetrical if left side of the graph is (roughly) mirror image of the right side
Shape
bell- shaped normal distribution
skewed - scores pile up on one side of the distribution, leaving “tail” of few extreme values on other side
positively skewed distribution
scores tend to pile up on left side of the distribution with tail tapering off to the right
negatively skewed distribution
scores tend to pile up on the right side + tail points to the left
Grouped Frequency Distribution
values in intervals ⇒ apparent limits of the interval
upper + lower boundaries involve real limits
Stem-and-Leaf Displays
stem-and-leaf display provides very efficient method for obtaining + displaying frequency distribution
Each score divided into stem consisting of first digit/digits, + leaf consisting of final digit
Stem-and-Leaf Displays
write leaf for each score beside its stem
organized picture of entire distribution
number of leafs beside each stem = frequency
individual leafs identify individual scores.
Percentile Ranks
relative location of individual scores within a distribution
percentage of individuals with scores equal to/less than X value
Interpolation
cumulative % identifies percentile rank for upper real limit
Interpolation
mathematical process based on assumption that scores + % change in regular, linear fashion as you move through interval from one end to other
Interpolation
- Find width of interval on both scales.
- Locate position of intermediate value in interval
fraction = distance from top of interval/interval width - Use fraction to determine distance from top of interval on other scale
distance = fraction x width (of scale we want to find) - Use distance from top to determine position on other scale
linear interpolation
“Assumption of linearity permits computation of intermediate percentile ranks and percentiles
Interpolation
single interval measured on 2 separate scales endpoints known
Given intermediate value on 1 of the scale task is to estimate corresponding intermediate value on other scale.
