TYPES OF HISTOGRAMS, SPSS, AND PYTHON

September 28, 2025

Once the observations are put into the bins, typically of equal width, the histogram shows the shape of the distribution of frequencies. Generally, there are no gaps in-between the bars in a histogram. A histogram and a bar graph are not similar. A histogram’s bar width has a distinct meaning. The Frequency histogram and the density histogram are the most commonly used types of histograms.

Frequency histogram

The height of a bar shows the frequency, which is the number of observations (values) in the bin. The bar width is the size of the bin (or interval).

The above histogram has 4 bins (0-25, 25-50, 50-75, and 75-100). The first bin (Bin₁: 0-25) has a frequency of 1, which means Bin₁ has only one observation (value).

The bin width can change the shape of a histogram. That means the same observations can be represented in different ways, by altering the bin size. However, one shape may better represent the center and spread than another.

Let's put the observations (example 8) into the bins of size 8.

Marks,  Xi	Frequency
28 ≤ Xi ˂ 36	5
36 ≤ Xi ˂ 44	3
44 ≤ Xi ˂ 52	2
52 ≤ Xi ˂ 60	1
60 ≤ Xi ˂ 68	3
68 ≤ Xi ˂ 76	4
76 ≤ Xi ˂ 84	4
84 ≤ Xi ˂ 92	4
92 ≤ Xi ˂ 100	1

SPSS Explore procedure summarized the values of "Subject (A) - Marks" (variable label). The following statistics appeared in the SPSS output viewer.

		Statistic
Subject (A) - Marks	Mean	56.391304
	Median	60.000000
	Std. Deviation	19.080545
	Minimum	28.000000
	Maximum	82.000000
	Range	54.000000
	Skewness	-0.105513

The above statistics are common to the following histograms. However, they were created using different bin sizes. The histograms represent the same observations, but they have different shapes. The shapes depend on the bin size. Histogram (1) has one mode (unimodal histogram). Histogram (2) has two modes (bimodal histogram) and shows that more than 50% of the students have 60 or above marks.

Histogram (1)

Histogram (2)

Let’s compare two histograms

The following statistics and the histogram (3) are the results of the example (9) produced by the SPSS Explore procedure. They appeared in the SPSS output viewer.

		Statistic
Subject (B) - Marks	Mean	56.391304
	Median	53.000000
	Std. Deviation	19.080545
	Minimum	30.000000
	Maximum	96.000000
	Range	66.000000
	Skewness	0.548684

Here, also note that the statistics—mean and standard deviation, of subject A are equal to the statistics of subject B.

Subject (A) - Marks	Subject (B) - Marks
Mean = 56.39	Mean = 56.39
Std. Dev. = 19.08	Std. Dev. = 19.08

Histogram (3)

Density histograms for comparing distributions

Density histograms make use of bar areas to show percentages. The width of each bar and the height indicate the percentage (instead of the number of observations) of the observations in each bin. The height is the frequency density. The total area of all the rectangles is equal to 1.

Histograms (4)

The following image, which was created with Python, shows two density histograms: (i). Subject _A histogram: Bimodal histogram (blue) and (ii). Subject _B histogram: Bimodal right-skewed distribution (positively-skewed). The histogram (i) is on top of the histogram (ii), sharing the same bins of size 11. Even though some statistics of both examples are equal, their shapes are not similar.

The dark area is common to the subject A and subject B marks. More students have obtained 60 or above marks for the subject A. The number of students with 40-60 marks is more for the subject B.