STAT 2-1: Frequency Distributions for Organizing and Summarizing Data

In statistics we are often interested in determining whether the data have a ___________ distribution.

normal

Relative Frequency Distribution (or Percentage Frequency Distribution)

Each class frequency is replaced by a relative frequency (or proportion) or a percentage.

Frequency Distribution (or Frequency Table)

Shows how data are partitioned among several categories (or classes) by listing the categories along with the number (or frequency) of data values in each of them.

Class Width

The difference between two consecutive lower class limits in a frequency distribution.

Upper Class Limits

The largest numbers that can belong to each of the different classes.

Class Boundaries

The numbers used to separate the classes, but without the gaps created by class limits.

Lower Class Limits

The smallest numbers that can belong to each of the different classes.

Class Midpoints

The values in the middle of the classes. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing by the sum of 2.

Procedure for Constructing a Frequency Distribution

1. Select the number of classes, usually between 5 and 20. 2. Calculate the class width. Class Width = (Maximum value) - (Minimum value)/(Number of Classes) Round this result to get a convenient number. (It's usually best to round up.) 3. Choose the value for the first lower class limit by using either the minimum value or a convenient value below the minimum. 4. Using the first lower class limit and class width, list the other lower class limits. 5. List the lower class limits in a vertical column and then determine and enter the upper class limits. 6. Take each individual data value and put a tally mark in the appropriate class. Add the tally marks to get the frequency.

The sum of the percentages in a relative frequency distribution must be very close to ___________ (with a little wiggle room for rounding errors).

100%

Percentage for a class (formula)

= ((frequency for a class)/(sum of all frequencies)) x 100%

Relative frequency for a class (formula)

= (frequency for a class)/(sum of all frequencies)