Chapter 2- Frequency Distributions: Lecture Flashcards
Frequency Distributions
- Show how often each category of a variable occurs
- Organize and simplify the dataset
- Show where each case is located relative to others in the sample or population
Frequency distribution tables
X-Column
- X Values from high to low
- only indicated values within range of your scores
Frequency distribution tables
f column
- tallies (or frequencies) are determined for each value
- how often each X occurs in the data set
- the sum of the frequencies=N (population) or n (sample)
Frequency distribution tables
Third column can be used for…
- Proportion (p) for each category: p=f/N, sum of p=1
- or Percentage corresponding to each X value: percentage=f/N times 100
Regular frequency distribution
frequency distribution table that lists all x values individually
Grouped frequency distribution
- frequency table that lists groups of scores (bc sometimes the list of X values is too long)
Class intervals
- used in grouped frequency distribution tables
- intervals have the same width, and are usually a simple number (2, 5, 10, etc)
- Interval width is selected so that the table will have around 10 intervals
frequency distribution graphs
- X values are listed on the X axis and Y values are listed on the y axis
- When the score categories (or variable of interest) are on an interval or ratio scale, graph should either be a histogram or polygon NOT a bar graph
Histograms
- A bar is centered above each score (or class interval in the case of grouped data)
- Height of the bar corresponds to the frequency of individuals that endorsed that particular score (or whose score fell into that class interval)
- Bars touch bc it’s meaningful (numerical order)
- Captures data in a way where people can quickly understand what is going on
Polygons
- a dot is centered above each score
- the height of the dot corresponds to the frequency
- dots are then connected by straight lines
- additional line is drawn at each end to bring the graph back to a 0 frequency (but not always)
bar graphs
- used for x values on a nominal or ordinal scale
- just like a histogram except that gaps are left between adjacent bars
smooth curve
- If scores or on the ratio or interval scale, it is customary to present distribution as a smooth curve rather than a jagged histogram or polygon
- emphasizes that the distribution is likely not showing the exact frequency for each category
- are useful because they show and summarize the entire set of scores
At a glance, what can a smooth curve determine?
- the highest and lowest score
- where scores are centered
- whether scores are clustered or scattered
smooth curves
the normal curve
- a symmetrical frequency distribution with the greatest frequency in the middle and frequencies decreasing as you move away from the middle in either direction
- frequently occurs in nature
symmetrical distribution
- the left side is roughly a mirror image of the right
- Ex. hill shaped normal distribution
skewed distribution
- scores pile up on one side of the distribution
- leaves a tail of a few extreme values on the other side
positive skew
scores pile on left, tail points right
negative skew
scores pile on the right, tail points left
percentile rank
the percentage of individuals with scores equal to or less than a given X value
percentile
when an x value is described by its rank, it is called a percentile
ex. Twenty-third percentile in hand size
stem-and-leaf display
- efficent method for displaying a frequency distribution
- stem contains first digit(s)
- leaf contains last digt
- only useful for small populations/samples bc each score is listed
