A histogram also called a frequency histogram could be defined as an accurate graphical representation of the distribution of numerical data set. It is an estimate of the probability distribution of a continuous variable which is why there are no gaps. Histogram differs from a bar graph in the sense that a bar graph relates two variables, but a histogram relates only one.
It is preferable to use a histogram instead of a bar graph when you have too many data points to plot individually.
Example: you want to use census data to make a graph of the number of people of each age at a home party. Before creating the histogram, you might first group together 0 − 14 year-olds, 15 − 29 year-olds, 30 − 49 year-olds, etc. Each of these ages intervals should have the same size or length.
Table 3.1. The distribution of people ages at a home party.
Relative frequency histogram
We can transform the data table 3.1 into a relative frequency histogram by converting the numbers into frequencies. Frequency histogram is the same as a regular histogram, except values are displayed as percentage of the total of the data.
Table 3.2. The frequency distribution of people ages at a home party.
A stem-and-leaf display or stem-and-leaf plot is just another way to present quantitative data in a graphical format, similar to a histogram because both types of charts group together data points, to assist in visualizing the shape of a distribution, they are very helpful ways in exploratory data analysis to visualize how many data points fall into a certain category or range.
Example: let’s say we have the finishing scores of golfers in a round of tournament golf: 66, 67, 67, 68, 68, 68, 68, 69, 69, 69, 69, 70, 70, 71, 71, 72, 73, 75, 101, 102, 111
|6||6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9|
|7||0, 0, 1, 1, 2, 3, 5|
Table 3.3. A stem plot of the scores, the “stems” are the numbers on the left whereas the “leaves” are those on the right
Key: 7|0 = 70