PS3 – Histograms and Stem-and-leaf plots

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.

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.

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

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

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