PsychStats- Chapter 2: : Frequency Distributions

1. Frequency Distributions and Frequency Distribution Tables 2. Grouped Frequency Distribution Tables 3. Frequency Distribution Graphs 4. Percentiles, Percentile Ranks, and Interpolation 5. Stem & Leaf Displays

frequency distribution

an arrangement of data that indicates how often a particular score or observation occurs

frequency distribution table

presents the number of times that each category of a qualitative variable or value is observed within a sample. for a large number of values it is common for the frequencies to be reported in ranges or intervals.

Grouped Frequency Distribution Tables

• If the number of categories is very large they are combined (grouped) to make the table easier to understand

• however , information is lost when categories are grouped

Frequency Distribution Graphs

organized list that enables us to see clusters or patterns in data.

quickly summarize data & attain level of meaning at a glance:

histograms and polygons.

Graphs for population distributions

• When a population is small, scores for each member are used to construct a frequency distribution graph such as a histogram and bar graph

• When the population is large, scores for each member are not possible --> graphs based on relative frequencies are used; graphs use smooth curves to indicate exact scores were not used

Shape of frequency distribution

symmetrical distribution , skewed distribution, tail of the distribution, positively skewed

symetrical distribution

it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other

skewed distribution

the scores tend to pile up toward one end of the scale and taper of gradually toward the other end.

tail of the distribution

the section where the scores taper off toward one end of a distribution

positively skewed

A distribution with the tail on the right-hand side is positively skewed because the tail points toward the positive (above-zero) end of the x-axis.

Rank or percentile rank of a score

defined as the percentage of individuals in the distribution with scores at or below the particular value.

Percentile

a point on a ranking scale of 0 to 100

cumulative frequency

The sums of the frequencies of the data values from smallest to largest.

cumulative percentage

the percentage of cases at or below any given value of the variable

Interpolation

an estimation of a value within two known values in a sequence of values

stem and leaf display

A multiple column table depicting the individual digits of the scores. It shows the range of values of the variable