Histogram

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.

Ages1-56-910-1314-1718-2122-25
Number511232494

Table 3.1. The distribution of people ages at a home party.

Figure 1. The way the data (people ages) is spread out in the histogram is called the distribution.

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.

Ages1-56-910-1314-1718-2122-25
Frequency0.06580.14470.30260.31580.11840.5263

Table 3.2. The frequency distribution of people ages at a home party.

Stem-and-leaf plot

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

StemLeaf
66, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9
70, 0, 1, 1, 2, 3, 5
101,2,11

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