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### Understanding Boxplots

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Social Studies - History. History World History. For All Subject Areas.The goal of Six Sigma is to improve the quality and productivity of a project team or company. In order to accomplish this goal, Six Sigma uses different chart aids to identify variation among data samples.

When a histogram or box plot is used to graphically represent data, a project manager or leader can visually identify where variation exists, which is necessary to identify and control causes of variation in process improvements. What Is a Histogram? A histogram is a type of bar chart that graphically displays the frequencies of a data set.

Similar to a bar chart, a histogram plots the frequency, or raw count, on the Y-axis vertical and the variable being measured on the X-axis horizontal. The only difference between a histogram and a bar chart is that a histogram displays frequencies for a group of data, rather than an individual data point; therefore, no spaces are present between the bars. Typically, a histogram groups data into small chunks four to eight values per bar on the horizontal axisunless the range of data is so great that it easier to identify general distribution trends with larger groupings.

What Is a Box Plot? A box plot, also called a box-and-whisker plotis a chart that graphically represents the five most important descriptive values for a data set. These values include the minimum value, the first quartile, the median, the third quartile, and the maximum value. When graphing this five-number summary, only the horizontal axis displays values. Within the quadrant, a vertical line is placed above each of the summary numbers. Although histograms and box plots are collectively part of the chart aid category, they do represent very different types of charts.

Both charts effectively represent different data sets; however, in certain situations, one chart may be superior to the other in achieving the goal of identifying variances among data. The type of chart aid chosen depends on the type of data collected, rough analysis of data trends, and project goals. A histogram is highly useful when wide variances exist among the observed frequencies for a particular data set.

As seen in the two graphs to the left, the histogram shows that there are three peaks within the data, indicating it is tri-modal three commonly recurring groups of numbers. This is important because to improve processes, it is critical to understand what is causing these three modes.

Had this data simply been graphed using a box plot, the values would average one another out, causing the distribution to look roughly normal. Another instance when a histogram is preferable over a box plot is when there is very little variance among the observed frequencies. The histogram displayed to the right shows that there is little variance across the groups of data; however, when the same data points are graphed on a box plot, the distribution looks roughly normal with a high portion of the values falling below six.

The final set of graphs shows how a box plot can be more useful than a histogram. This occurs when there is moderate variation among the observed frequencies, which causes the histogram to look ragged and non-symmetrical due to the way the data is grouped. This may lead one to assume the data is slightly skewed.The image above is a boxplot. It can tell you about your outliers and what their values are. It can also tell you if your data is symmetrical, how tightly your data is grouped, and if and how your data is skewed.

This tutorial will include:. As always, the code used to make the graphs is available on my github. You need to have information on the variability or dispersion of the data. A boxplot is a graph that gives you a good indication of how the values in the data are spread out. Although boxplots may seem primitive in comparison to a histogram or density plotthey have the advantage of taking up less space, which is useful when comparing distributions between many groups or datasets. The next section will try to clear that up for you.

The image above is a comparison of a boxplot of a nearly normal distribution and the probability density function pdf for a normal distribution. The reason why I am showing you this image is that looking at a statistical distribution is more commonplace than looking at a box plot. In other words, it might help you understand a boxplot. This section will cover many things including:. This part of the post is very similar to the 68—95— To be able to understand where the percentages come from, it is important to know about the probability density function PDF.

A PDF is used to specify the probability of the random variable falling within a particular range of valuesas opposed to taking on any one value. The equation below is the probability density function for a normal distribution. This can be graphed using anything, but I choose to graph it using Python. The graph above does not show you the probability of events but their probability density. To get the probability of an event within a given range we will need to integrate.

Suppose we are interested in finding the probability of a random data point landing within the interquartile range. This can be done with SciPy. As mentioned earlier, outliers are the remaining. This section is largely based on a free preview video from my Python for Data Visualization course.

The code below reads the data into a pandas dataframe. There are a couple ways to graph a boxplot through Python. You can graph a boxplot through seaborn, pandas, or seaborn. The boxplots you have seen in this post were made through matplotlib. This approach can be far more tedious, but can give you a greater level of control. You can plot a boxplot by invoking. Data science is about communicating results so keep in mind you can always make your boxplots a bit prettier with a little bit of work code here.

Here are a few other things to keep in mind about boxplots:. Future tutorials will take some this knowledge and go over how to apply it to understanding confidence intervals. If you any questions or thoughts on the tutorial, feel free to reach out in the comments below, through the YouTube video pageor through Twitter. Sign in. Understanding Boxplots.

Michael Galarnyk Follow. Towards Data Science A Medium publication sharing concepts, ideas, and codes. Towards Data Science Follow.Box plots are drawn for groups of W S scale scores. They enable us to study the distributional characteristics of a group of scores as well as the level of the scores.

To begin with, scores are sorted. Then four equal sized groups are made from the ordered scores. The lines dividing the groups are called quartilesand the groups are referred to as quartile groups. Usually we label these groups 1 to 4 starting at the bottom. Median The median middle quartile marks the mid-point of the data and is shown by the line that divides the box into two parts. Half the scores are greater than or equal to this value and half are less.

The range of scores from lower to upper quartile is referred to as the inter-quartile range. Upper quartile Seventy-five percent of the scores fall below the upper quartile. Lower quartile Twenty-five percent of scores fall below the lower quartile. Whiskers often but not always stretch over a wider range of scores than the middle quartile groups.

Box plots are used to show overall patterns of response for a group. They provide a useful way to visualise the range and other characteristics of responses for a large group. The diagram below shows a variety of different box plot shapes and positions. Understanding and interpreting box plots. Definitions Median The median middle quartile marks the mid-point of the data and is shown by the line that divides the box into two parts.

This suggests that overall students have a high level of agreement with each other. This suggests students hold quite different opinions about this aspect or sub-aspect. For example, the box plot for boys may be lower or higher than the equivalent plot for girls. Any obvious difference between box plots for comparative groups is worthy of further investigation in the Items at a Glance reports. Your school box plot is much higher or lower than the national reference group box plot.

This shows that many students have similar views at certain parts of the scale, but in other parts of the scale students are more variable in their views.

The long upper whisker in the example means that students views are varied amongst the most positive quartile group, and very similar for the least positive quartile group. The medians which generally will be close to the average are all at the same level. However the box plots in these examples show very different distributions of views. It always important to consider the pattern of the whole distribution of responses in a box plot.A box and whisker plot is a summarized graph summarizing, the five numbers, minimum, lower quartile, median, upper quartile and maximum.

While the portion covering lower quartile, median and upper quartile appears as a box, minimum and maximum data points show up as whiskers at the two ends see figure below. Obviously, while its total length indicates range of the data, the size of the box indicates interquartile range. Let us now try to compare two date sets A and B, whose box and whisker chart is given below. From this we observe that. How would you compare two box and whisker plots?

Statistics Organizing and Summarizing Data Boxplots. Shwetank Mauria. Jan 18, Please see below. Explanation: A box and whisker plot is a summarized graph summarizing, the five numbers, minimum, lower quartile, median, upper quartile and maximum. From this we observe that 1 It is apparent that Data set A has a larger range suggesting that it has the worst and the best of the two. Related questions Do box plots show outliers?

What is another name for a boxplot? Is the median always in the exact middle of a boxplot? How would I find the 5-number summary for the data set: 54, 9, 37, 15, 52, 40, 54, 78, 1, 3, 26, 26, 37? How does the interquartile range relate to percentiles? What does the interquartile range tell us? What is a modified boxplot? How do you identify outliers when displaying data in a boxplot? How is the 5-number summary used in constucting a boxplot? Box and whisker plot? The data set 5,6,7,8,9,9,9,10,12,14,17,17,18,19,19 represents the number See all questions in Boxplots.

Impact of this question views around the world. You can reuse this answer Creative Commons License.BioTuring's Blog. Box plots, a. They manage to carry a lot of statistical details — medians, ranges, outliers — without looking intimidating. But box plots are not always intuitive to read. How do you compare two box plots? The key information you want to get when reading box plots is: are these groups different, and if so, how? To quickly compare box plots, look for these things:. Start with the boxes.

They represent the interquartile range, or the middle half of the values in each group. Non-overlapping boxes, groups are different. If they overlap, move on to the lines inside the boxes. If both median lines lie within the overlap between two boxes, we will have to take another step to reach a conclusion about their groups.

The lines coming out from each box extend from the maximum to the minimum values of each set. Together with the box, the whiskers show how big a range there is between those two extremes.

Larger ranges indicate wider distribution, that is, more scattered data. The same thing can be said about the boxes. Short boxes mean their data points consistently hover around the center values. Taller boxes imply more variable data. Wider ranges whisker length, box size indicate more variable data.

When there are outliers, they are dotted outside the whiskers. Not all datasets have outliers. Data points have to go above or below the box pretty far to count as outliers. How far? First, look at the boxes and median lines to see if they overlap. Then check the sizes of the boxes and whiskers to have a sense of ranges and variability.

Finally, look for outliers if there are any. If you want to know what else is in the box hah, see what I did there? For RNA sequencing data Hera.Comparing box plots worksheet :. Worksheet on c omparing box plots is much useful to the students who would like to practice problems on comparing box plots.

## Comparing Box Plots and Histograms – Which Is the Better Tool?

Problem 1 :. Questions :. Compare the shapes of the box plots. Compare the centers of the box plots. Compare the spreads of the box plots. Explain how you know. Problem 2 :. Answers for the questions in problem 1 :. The positions and lengths of the boxes and whiskers appear to be very similar. In both plots, the right whisker is shorter than the left whisker. This means that the median shopping time for Group A is 7. The box shows the interquartile range. The boxes are similar.

Answers for the questions in problem 2 :. Store A has a greater spread. Store B had a greater number of sales overall. After having gone through the stuff given above, we hope that the students would have understood "Comparing box plots worksheet".

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