In this video, I will show you how to make and interpret a histogram and a boxplot. These are two types of graphs and graphs are often used to quickly and easily understand the measurements of a variable that you have. The histogram and boxplot are graphs for a numerical variable. In another video, I will show you how to make graphs for categorical variables. When you have a numerical variable, the histogram and the boxplot are the most popular methods for visualization of this variable. Let's reuse the example of cross-border money transactions. If mistakes are made, a client submits a reclaim. This is what the data look like. I will now show you how to make a histogram and a boxplot in Minitab over a variable, total time. So pause the video, load this data into Minitab before you continue. I have copied the variable total time into Minitab here. To make a histogram or a boxplot, we have to go to the menu graph. You'll find the histogram here. We will make a simple histogram, but you can also choose to make one with fit and then you get the normal distribution. Simple it is, for now. Okay, there we go. You select total time, which is the variable you want to graph. Okay, and you get a histogram. For a box plot, we go back to graph again, and you go to box plot. You can select a simple one because we have one variable, okay. We want to graph the total time. Okay. Now we have a boxplot of total time, and we have a histogram of total time. Let's study these two graphs. This is the histogram and it is used to give a quick impression of a numerical variable. A histogram is composed of so-called bins. The height of the bins represents frequencies. The horizontal axis depicts the variable total time. The first bin reaches around 130, and represents a total time around zero. That is, roughly 130 data values have a value around zero. You see, the bin height decreases towards the right. This means that larger total times are more scarce, total times of 45 days or higher rarely occur. Histograms can be used to review interesting patterns in your data. It can be use to see whether your data is symmetrical or skewed, or even whether it is bimodal. Bimodality typically occurs when two distinct populations are present in the sample, giving a mixture of distributions. For example, you might be measuring shoe sizes. Then the left peak will be the female shoe sizes, and the right peak will be the male shoe sizes. Data usually has tails, which are clearly visualized in a histogram. The larger part of the data that is concentrated together is called the bulk. And the remaining parts on both sides are called the tails. Tails decrease outwards. So, that was the histogram. Now, let's take a look at the boxplot. In the video on descriptive statistics, we discussed quartiles and the median. These effectively divided data set into four equal parts. This can be shown in a boxplot. It shows you the median, the bulk, the whiskers, and possibly outliers. Let's look at an example. A boxplot consists of a box which is the middle 50% of your data, that is 25% of the data is smaller and 25% of the data is larger. These are indicated by the whiskers. If there are observations that are far away from the box, these observations are called outliers and are indicated with a star. A boxplot reveals where the data are located on the real line. It shows you the minimum value and the maximum value. If there's one outlier, as in this example, then the second highest value determines where the whisker will stop. The boxplot also shows you the interquartile range. The interquartile range is equal to the length of the box. And that is equal to the difference between the third quartile and the first quartile, also see the video on descriptive statistics for more details on quartiles. The boxplot shows you the total range which is equal to the maximum minus the minimum. Now, let's go back to our data example. This is the boxplot we made for the total time. 50% of the data is smaller than the median, which equals approximately four. So we can conclude that half of our claims is handled within four days. 75% of the data is smaller than 12 days. So 75% of the claims is handled within 12 days. The boxplot also shows a very short whisker at the bottom and a very long whisker at the top as well as many outliers to the top of box. This shows you that the distribution of this variable is skewed, which we have also seen in the histogram. In summary, you can make a histogram or a boxplot to visualize a numerical variable. A histogram shows you the variable and gives you information about the distribution of your data. A box plot gives you also information about the spread in your data and about outliers.
