Definition
A histogram is a plot that lets you discover, and show, the underlying frequency distribution of a set of continuous data allowing the inspection of data for its underlying distribution . The common distribution shape can be normal distribution, outliers, skewness, etc.
Continuous data refers to data that can take any value within a given range. It can be measured with great precision and includes decimal or fractional values. Continuous data is essentially infinite and allows for a smooth and unbroken spectrum of possibilities. Examples of continuous data include height, weight, temperature, and distance.
Histogram is a bar graph where the area of the bars are used to represent the frequencies. Unlike in bar graphs, there are no gaps between adjacent bars.
Unlike in bar graphs where class limits are on horizontal axis, in histogram we must use the lower and upper class boundaries which must be clearly marked on the horizontal axis with an accurate scale.
The width of each bar in histogram is proportional to the class width.
Example
The following are masses of some 30 patients that visited a health center in a certain day.
33 45 49 45 60 67 57 49 48 43 59 64 39 38 44 55 45 48 52 55 54 57 56 49 55 56 39 42 41 46.
- Present the information in a frequency table
- Draw a histogram to represent the information
solution
We start by first determining the number of classes required
Range = 67-33=34
A class size of 5 will give 34/5 = 6.8 ≈ 7
The frequency table will be as follow
The measurements are usually the estimates of the actual measurements. so that a measurements of 33 kg could be around 32.5kg and 33.4 kg
In the above example, all classes have equal class width, hence it will be like a bar graph.
To draw a histogram, we consider the lower and the upper class boundaries of each class, which becomes the boundaries of the bars.
The bars are equal in width but heights corresponds to the frequencies. The histogram is a shown.
Practice question
The frequency table below shows the measurements of girths of 30 trees in a forest in centimeters
| Class | Frequency |
|---|---|
| 60-64 | 8 |
| 65-69 | 14 |
| 70-79 | 16 |
| 80-89 | 10 |
| 90-94 | 7 |
Using a suitable scale, draw a histogram to represent this information.
After working it out, check whether your resultant histogram is like the one in figure below
n a histogram, each bar’s size shows how many times something happened in a specific range. The height alone doesn’t tell the full story but it is the combined height and width of the bar that gives the complete picture. Height alone shows how often things occur only when all the bars are the same width. If the bars have different widths, you need to look at both the height and the width to understand the frequency.
Difference between a bar chart and a histogram
The major difference is that a histogram is only used to plot the frequency of score occurrences in a continuous data set that has been divided into classes called bins. Bar charts, on the other hand, can be used for a great deal of other types of variables, including ordinal and nominal data sets.
Related Topics and pages
- Frequency tables
- bar graphs
- pie charts
- Line graphs
- Grouped and ungrouped data
- Frequency polygon
- Histograms
- Measures of Central tendency
- Mean for grouped data
- Working with the assumed mean
- Quartiles, Deciles and percentiles
- Measures of dispersion
- Variance
- Physics
