Frequency Distributions

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Frequency Distributions

Number of Friends	f	rf	%	cf	crf	c%
5	1	.08	8	12	1.00	100
4	2	.17	17	11	.92	92
3	4	.33	33	9	.75	75
2	3	.25	25	5	.42	42
1	2	.17	17	2	.17	17

Example: A group of 12 college students is asked to indicate the number of close friends that they have. They all report having from 1 to 5 close friends.

We begin by listing the obtained score values from highest to lowest.

Absolute frequencies are simply a count of # of individuals who received each score.

Derive absolute frequencies (f) by counting the number of individuals who received each score, and indicate the frequencies next to the corresponding score values.

- e.g., above, 3 people reported having 2 close friends

Relative frequencies represent the proportion of time that a given score occurred.

Derive relative frequencies (rf) by dividing the count for a given score by the total number of scores.

- e.g., above, divide 3 by 12, to get .25

Percentage simply reflects the percentage of time that a given score occurred.

Derive percentage by multiplying rf by 100

– e.g., above multiply .25 by 100 to get 25%

Cumulative frequencies allow us to tell at a glance the number of scores that are equal to or less than a given score.

Derive cumulative frequencies (cf) by adding the count in a given row to those in the rows below it.

- e.g., above, we add the 3 people who reported having two friends to the 2 people who reported having one friend – so we know 5 people said they had two or fewer friends

Cumulative relative frequencies tell us the proportion of individuals who have a given score or lower.

Derive cumulative relative frequencies (crf) by dividing the cf by the total number of observed scores.

- e.g., above, for the score of 2, take the cf of 5 and divide by 12, to get .42

Cumulative percentages are simply the percentage of people at that score or lower.

Derive cumulative percent (c%) by multiplying the crf by 100

– e.g., multiply .42 by 100 to get 42%

Grouped Scores

Example: Study examining the age of women who seek support at a battered women’s shelter. A clinical psychologist who works at the clinic wants to get a sense for the age for clients he/she will be seeing. A total of 200 women are interviewed and report their age.

We could construct a table like this:

Age	f	rf	%	cf	crf	c%
30-45	38	.19	19	200	1.00	100
15-29	162	.81	81	162	.81	81

But, the above table is not very informative since it provides little insight into how the individuals differed in their age.

To construct a useful table, we need to determine the three following characteristics: how many groups do we want, what interval size should we use for the groups, and where should the lowest interval begin (see guidelines below)

We start by deciding we want 5 groups. The lowest age was 15 and the highest age was 44, thus (44-15)/5 = 5.8, which we round to 5 because 6 is not an accepted interval size. The beginning score is 15, yielding the following groups:

Age	f	rf	%	cf	crf	c%
40-44	2	.01	1	200	1.00	100
35-39	12	.06	6	198	.99	99
30-34	24	.12	12	186	.93	93
25-29	42	.21	21	162	.81	81
20-24	66	.33	33	120	.60	60
15-19	54	.27	27	54	.27	27

General Guidelines for Constructing Frequency Tables with Grouped Data

Number of groups – rule of thumb, 5 to 15 groups tends to strike balance between imprecision and incomprehensibility in most instances. If number of possible score values is small, fewer groups can be used; if number of possible score values is large, more groups are required.

Size of interval – typically, use interval size of 2, 3, or multiple of 5 is used.

- To determine interval size: 1) subtract lowest score from highest score, 2) divide this difference by desired # of groups, 3) result rounded to nearest to commonly used interval-size values.

** in the above example, we use a total of 6 groups in order to keep our interval size = 5

Beginning of lowest interval – conventional starting point is the closest number evenly divisible by the interval size that is equal to or less than the lowest score.