Frequency Graphs

 

-     Picture is worth a thousand words – often displaying our information in a graphical format is a concise way to present it.

 

Frequency Graphs (2.5)

-     Way of reporting data graphically.  Usually more impactful than frequency distributions.

 

-     Frequency Histogram

-     X axis – abscissa – lists the score values from low to high, extending from one unit below the lowest score to one unit above the highest score.

-     Y axis – ordinate – represents the frequency w/which each score occurred

-     Label that clearly names the variable in study should appear beneath the score values.

-     Generally speaking, a graph should stand alone so that anyone who looks at it can readily interpret it.

 

-     Frequency Polygon

-     Similar to frequency histogram – uses same ordinate and abscissa

-     Major difference:  Bars aren’t used, rather dots corresponding to appropriate frequencies placed directly above score values

-     Dots connected by solid lines

-     Always “closed” with the abscissa in that they always include a value that is a unit higher than the highest observed value and a unit lower than the lowest observed score, with a frequency of 0 for each.

-     No specific rules govern when a frequency histogram as opposed to a frequency polygon should be used.

-     Polygons are typically used when variables being reported are continuous, histogram is used when variables are discrete.

-     Frequency polygon tends to highlight the “shape” of the entire distribution more than the frequency histogram does.

-     Frequency histogram tends to highlight the frequency of occurance of specific scores rather than the entire distribution.

 

-     Line Plot

-     Constructed exactly like the frequency polygon, except that it is not “closed”

-     Left and rightmost points of the line end on the lowest and highest scores, respectively.

 

-     Multiple groups

-     Can construct line plots and histograms with multiple groups (same variable on more than one group)

-     Becomes unwieldy for more than two groups.

 

-     Grouped v. ungrouped scores

-     Can construct line plots and histograms and polygons for grouped and ungrouped scores

-     When scores are grouped, abscissa might list the midpoints of the score intervals rather than the score values.

-     Alternatively, the intervals for the groups may be presented.

 

-     Stem and Leaf plots

-     Compact way of conveying both the individual scores that occurred and the general “shape” of the frequency distribution

-     Somewhat like a frequency distribution turned on its side

-     Useful as long as the number of scores is not too large and the number of different values of the base is reasonable.

-     More than one or two groups, but less than 20

-     All values from the ones place go on the leaves

 

-     Frequency Graphs for Qualitative Variables

-     Bar Graphs

-     Values of the variable are listed on the abscissa, frequencies are listed on the ordinate

-     Major difference from frequency histogram is that the bars are drawn such that they do not touch one another.

-     Because each bar represents a distinct category.

 

Misleading Graphs (2.6)

-     Presentation of data in graphic form can be highly informative, but it can also be misleading.

-     Rules to reduce misleading graphs:

-     Ordinate height for highest frequency should be ¾ to 2/3 length of abscissa

-     Ordinate should start w/frequency of zero and “jumps” indicated by zigzag if not drawn to scale.

-     Rules ensure uniform, clearly interpretable presentation of graphed results.

 

Graphs of Relative Frequencies, Cumulative Frequencies, and Cumulative Relative Frequencies (2.7)

-     Relative frequency histograms and polygons will have an identical shape as frequency histograms and polygons for the same set of scores.

-     Cumulative frequency graphs

-     Solid dots representing cumulative frequencies placed above upper real limit of each score value.

-     Cumulative frequency curve always remains level or increases as it moves from left to right.

-     Because cumulative frequency for given score value is always equal to or greater than the cumulative frequency of the preceding score value.

 

-     Cumulative relative frequencies can be represented in a graph.

-     Graph would take identical shape as corresponding cumulative frequency graph, but would have ordinate labeled crf and demarcated with cumulative relative frequency values.