Chapter 2: Frequency Distributions

• A frequency distribution:

  • Shows the _____ of individuals located in each category on the scale of measurement

Shows the # of individuals located in each category on the scale of measurement

• A frequency distribution:

  • Can be either a ____ or a _____

• table or a graph

• Structure of a frequency distribution table:

  • Frequency count (___) next to category (___ values)

• (f)

• X

• Structure of a frequency distribution table:

  • Σ__ = N

• f

• Proportions:

  • Measures the _______ of the total group that is associated with each score

• fraction

• Proportions:

  • p =

f / N

• Proportions:

  • Called ______ _________because they describe the frequency (f) in relation to the total number (N)

• relative frequencies

• Percentages:

Expresses relative frequency out of 100

• Percentages:

  • equation-

p(100) = f / N (100)

Use the frequency distribution table to determine how many participants were in the study.

10

True or False:

• More than 50% of the individuals scored above 3.

True

True or False:

• The proportion of scores in the lowest category was p = 3.

False

• Frequency Distribution Tables:

  • What should you do if the number of categories is too large?

Group the categories into intervals. 

AKA a Grouped Frequency Distribution Table

• Frequency Distribution Tables:

  • What info is lost when categories are grouped

• Individual scores cannot be retrieved

• The wider the grouping interval, the more information is lost

• Frequency Distribution Tables:

  • Guidelines:

• Ten or fewer class intervals is typical (but use good judgment for the specific situation)

• The width of each interval should be a relatively simple number (e.g., 2, 5,10, or 20)

• All intervals should be the same width (other than for an open category)

• True or False:

  • You can determine how many individuals had each score from a frequency distribution table.

True

• True or False:

  • You can determine how many individuals had each score from a grouped frequency distribution.

False

• Graphs

  • The bar for continuous variables- the ____ of the bar extends to the real limits of the category (remember rounding)

• width

Explain a “block” Histogram

Each block represents one person

What graph to use for nominal and ordinal data (non-numerical scores)?

A bar graph

• Bar graphs for Nominal and ordinal data (non-numerical scores)

  • In a regular bar graph is the area of the bars meaningful?

No! Only the height is meaningful

• Bar graphs for Nominal and ordinal data (non-numerical scores)

  • What do spaces between bars represent?

Spaces between bars indicate discrete categories

• Bar graphs for Nominal and ordinal data (non-numerical scores)

  • Bar graphs without a particular order would be for ______ data

• Nominal

• Bar graphs for Nominal and Ordinal data (non-numerical scores)

  • Bar graphs without measurable width would be for ______ data

• Nominal and Ordinal data

• Graphs for Population Distributions

  • Describe a Normal Distribution:

Symmetric with greatest frequency in the middle

Common data structure for many variables

What does this show?

The population distribution of IQ scores: an example of a Normal Distribution

• Shape of a Frequency Distribution

  • Symmetrical distribution:

Each side is a mirror image of the other

• Shape of a Frequency Distribution

  • Skewed distribution:

scores pile up on one side and taper off in a tail on the other

• Shape of a Frequency Distribution

  • Skewed distribution:

    • Tail on the right (___ scores) = ____ skew

    • Tail on the left (____ scores) = _____skew

• (high) = positive

• (low) = negative

Label the graphs

What is the shape of this distribution?

positively skewed

• True or False:

  • It would be correct to use a histogram to graph parental marital status data (single, married, divorced...) from a treatment center for children

• False

  • Histogram = continuous data only. Marital status is categorical (nominal), so you’d use a bar chart, not a histogram.

• True or False:

  • It would be correct to use a histogram to graph the time children spent playing with other children from data collected in a children’s treatment center.

• True

  • Time is continuous/quantitative → a histogram is the correct choice.