Figure 2.4.4 Bar graph for the data in Example 2.4.4.
MINITAB
Using MINITAB, the bar chart is constructed by taking the following steps.
1 Enter the category in column C1.
2 Enter frequencies of the categories in C2.
3 From the Menu bar select Graph Bar Chart. This prompts the following dialog box to appear on the screen:
4 Select one of the three options under Bars represent, that is, Counts of unique values, A function of variables, or Values from a table, depending upon whether the data are sample values, functions of sample values such as means of various samples, or categories and their frequencies.
5 Select one of the three possible bar charts that suits your problem. If we are dealing with only one sample from a single population, then select Simple and click OK. This prompts another dialog box, as shown below, to appear on the screen:
6 Enter C2 in the box under Graph Variables.
7 Enter C1 in the box under Categorical values.
8 There are several other options such as Chart Option, scale; click them and use them as needed. Otherwise click OK. The bar chart will appear identical to the one shown in Figure 2.4.4.
USING R
We can use built in ‘barplot()’ function in R to generate bar charts. First, we obtain the frequency table via the ‘table()’ function. The resulting tabulated categories and their frequencies are then inputted into the ‘barplot()’ function as shown in the following R code.
DefectTypes = c(2,1,3,1,2,1,5,4,3,1,2,3,4,3,1,5,2,3,1,2,3,5,4,3, 1,5,1,4,2,3,2,1,2,5,4,2,4,2,5,1,2,1,2,1,5,2,1,3,1,4) #To obtain the frequencies counts = table(DefectTypes) #To obtain the bar chart barplot(counts, xlab=‘Defect type’, ylab=‘Frequency’)
2.4.4 Histograms
Histograms are extremely powerful graphs that are used to describe quantitative data graphically. Since the shape of a histogram is determined by the frequency distribution table of the given set of data, the first step in constructing a histogram is to create a frequency distribution table. This means that a histogram is not uniquely defined until the classes or bins are defined for a given set of data. However, a carefully constructed histogram can be very informative.
For instance, a histogram provides information about the patterns, location/center, and dispersion of the data. This information is not usually apparent from raw data. We may define a histogram as follows:
Definition 2.4.1
A histogram is a graphical tool consisting of bars placed side by side on a set of intervals (classes, bins, or cells) of equal width. The bars represent the frequency or relative frequency of classes. The height of each bar is proportional to the frequency or relative frequency of the corresponding class.
To construct a histogram, we take the following steps:
1 Step 1. Prepare a frequency distribution table for the given data.
2 Step 2. Use the frequency distribution table prepared in Step 1 to construct the histogram. From here, the steps involved in constructing a histogram are exactly the same as those to construct a bar chart, except that in a histogram, there is no gap between the intervals marked on the horizontal axis (the ‐axis).
A histogram is called a frequency histogram or a relative frequency histogram depending on whether the scale on the vertical axis (the
Example 2.4.5 (Survival times) The following data give the survival times (in hours) of 50 parts involved in a field test under extraneous operating conditions.
| 60 | 100 | 130 | 100 | 115 | 30 |
|
145 | 75 | 80 | 89 | 57 | 64 | 92 | 87 | 110 | 180 |
| 195 | 175 | 179 | 159 | 155 | 146 | 157 | 167 | 174 | 87 | 67 | 73 | 109 | 123 | 135 | 129 | 141 |
| 154 | 166 | 179 | 37 |
|
|
|
89 |
|
|
