Zach’s facts have been extracted from the book to remind you of the key concepts you and Zach have learned in each chapter.

Zach's Facts 3.1 Frequency distributions

• A frequency distribution can be either a table or a chart that shows each possible score on a scale of measurement along with the number of times that score occurred in the data.
   
• It displays each score alongside how many times that score occurred (the frequency).
   
• The relative frequency is the frequency (f) of a score divided by the total number of observed scores (N).
   
• The relative frequency can be expressed as a percentage by multiplying it by 100.
   
• The cumulative frequency of a score is the frequency of all scores up to and including that score.
   
• The cumulative percentage of a score is the percentage of all scores up to and including that score.
   

Zach's Facts 3.2 Grouped frequency distributions

• When there is a wide range of scores, use a grouped frequency distribution.
   
• To create one, divide the scale of measurement into equal parts known as class intervals.
   
• You want enough intervals that you retain the pattern within the data, but not so many that the frequency distribution is unmanageable; between 5 and 15 is typical.
   
• The intervals must not overlap; for example, you could not have intervals of 5–7 and 7–9 because both of these intervals contain the value 7.
   
• The intervals must contain all values of the scale of measurement. For example, you could not have intervals of 5–7 and 9–11 because the value 8 is entirely missing.
   
• Consider making the interval width a simple number such as 2, 5, 10 or a multiple of 5 or 10.
   
• The lower boundary of the interval should be a multiple of the width. For example, if the width is 5, then the intervals should start on 0, or a multiple of 5 such as 5, 10, or 25.
   

Zach's Facts 3.3 Histograms, polygons and bar graphs

• When you have a scale of measurement that is interval or ratio, you can use a histogram and frequency polygon to display the frequency of scores.
   
• These graphs display the possible scores of the measured variable on the x-axis, and the frequency with which each score occurs on the y-axis.
   
• Histograms plot the frequencies as bars rising up from the x-axis, whereas polygons plot them as points that are connected by straight lines.
   
• Bar graphs display categories of a nominal or ordinal variable along the x-axis, with bar heights representing the magnitude of a statistic plotted on the y-axis (this statistic could be the frequency, an average, etc.).