Frequency Distributions

Overview

Frequency distributions are graphical ways of summarizing a group of data. To understand what this means in simple terms, let’s use an example (again, this is the same example used in the statistical guides, Measures of Central Tendency and Measures of Spread).

Setting the Scene

A tutor set a piece of coursework for 100 students. The students could achieve a score between 0 and 100. The following marks were achieved:

62	81	49	47	69	52	77	45	57	64
71	60	51	58	40	39	44	40	67	64
63	81	74	74	49	83	81	49	71	76
84	37	39	48	66	42	79	45	74	61
85	51	52	38	67	42	69	69	55	62
80	42	68	74	53	64	75	40	75	64
51	35	41	49	57	81	77	67	54	70
74	39	42	56	51	45	39	84	67	81
41	63	59	39	62	53	58	81	55	45
42	37	72	65	71	70	40	40	44	40

This group of data can be graphically illustrated on a frequency distribution (or histogram) by showing how often (in order words, how frequently) students achieved different scores. For example, how many students scored 35 out of 100 or 64 out of 100? Looking again at the group of data below, one student scored 35 (numbers in red) whilst four scored 64 (numbers in blue).

62	81	49	47	69	52	77	45	57	64
71	60	51	58	40	39	44	40	67	64
63	81	74	74	49	83	81	49	71	76
84	37	39	48	66	42	79	45	74	61
85	51	52	38	67	42	69	69	55	62
80	42	68	74	53	64	75	40	75	64
51	35	41	49	57	81	77	67	54	70
74	39	42	56	51	45	39	84	67	81
41	63	59	39	62	53	58	81	55	45
42	37	72	65	71	70	40	40	44	40

Whilst this data can be presented in a tabulated format, we can also illustrate it graphically in a histogram. The histogram highlights the frequency (in other words, the number of times) that each mark was scored. In so doing, it shows the distribution and pattern of marks from the lowest to the highest. In our example, the scores the students achieved appear on the horizontal axis and the frequency that each of these scores occurred appears on the vertical axis (see below).



The shape and size of frequency distributions can vary considerably depending on the group of data that is being represented. Some of the most common types of frequency distribution are explained below.