Draw a Box Good for Construction
Typically, statisticians are going to apply software to help them look at data using a box plot. Notwithstanding, when you are first learning about box plots, it can be helpful to learn how to sketch them by hand. This way, yous volition be very comfortable with understanding the output from a computer or your calculator. In the following lesson, we will await at the steps needed to sketch boxplots from a given data set up.
Example information
Remember, the goal of any graph is to summarize a data ready. There are many possible graphs that one can use to practice this. One of the more mutual options is the histogram, only there are also dotplots, stem and leaf plots, and as we are reviewing here – boxplots (which are sometimes called box and whisker plots). Similar a histogram, box plots ignore information about each individual data value and instead show the overall pattern.
To review the steps, we will use the information set below. Let's suppose this information ready represents the salaries (in thousands) of a random sample of employees at a small company.
| 7 14 14 fourteen 16 | 18 20 20 21 23 | 27 27 27 29 31 | 31 32 32 34 36 | twoscore xl 40 xl 40 | 42 51 56 60 65 |
Steps to Making Your Box plot
Step i: Calculate the five number summary for your data prepare
The five number summary consists of the minimum value, the first quartile, the median, the tertiary quartile, and the maximum value. While these numbers can also exist calculated by hand (here is how to calculate the median past manus for example), they tin can chop-chop be found on a TI83 or 84 calculator under 1-varstats. The video below shows you how to become to that menu on the TI84:
For this data gear up, you will get the following output:
Pace 2: Identify outliers
Other than "a unique value", there is non ONE definition beyond statistics that is used to find an outlier. As you study statistics, you lot volition see that unlike settings will employ different techniques to flag or mark a potential outlier. With boxplots, this is done using something called "fences". The idea is that anything outside the fences is a potential outlier and shouldn't be included in the main group that we graph. Instead it volition be marked with a asterisk or other symbol.
The lower fence
Any data value smaller than the lwoer fence will be considered an outlier. The lower argue is defined past the following formula:
\(\text{lower fence} = Q_{one} – 1.5(IQR)\)
This formula makes utilise of the IQR, or interquartile range. This is defined as:
\(\text{IQR} = Q_3 – Q_1\)
Using the figurer output, nosotros have for this data set \(Q_1 = xx\) and \(Q_3 = 40\). This gives u.s.a.:
\(\brainstorm{align} \text{IQR} &= Q_{3}-Q_{one}\\ &= forty – 20\\ &= 20\end{align}\)
and using this value:
\(\begin{align} \text{lower contend} &= Q_{1} – ane.5(IQR) \\ &= 20 -1.v(20)\\ &= 20 – 30\\ &= -10\end{align}\)
Since there are no values in the data set that are less than -10, in that location are no lower (small) outliers.
The upper contend
Similar to the lower debate, anything data value larger than the upper argue volition be considered an outlier. This is defined by the post-obit formula.
\(\text{upper contend} = Q_{3} + one.5(IQR)\)
Using the calculation above, we know that \(\text{IQR} = twenty\). Nosotros also had \(Q_3 = twoscore\). Therefore:
\(\begin{marshal}\text{upper fence} &= Q_{three} + 1.5(IQR)\\ &= twoscore + 1.5(20) \\ &=forty + 30\\ &= 70\finish{marshal}\)
The largest value in the data set is 65, so this means at that place is no upper (big) outlier.
Since at that place were no small or large outliers in the gear up, we tin conclude in that location are no outliers overall.
Step 3: Sketch the box plot using the model below
The main part of the box plot volition be a line from the smallest number that is non an outlier to the largest number in our data set that is not an outlier. If a data set doesn't have any outliers (like this i), then this will just be a line from the smallest value to the largest value. The rest of the plot is made past drawing a box from \(Q_{i}\) to \(Q_{3}\) with a line in the middle for the median. Every bit a general instance:
Additionally, if you lot are drawing your box plot by hand you must think of calibration. In this data set, the smallest is 7 and the largest is 65. So starting the calibration at 5 and counting by 5 up to 65 or 70 would probably give a dainty picture. Then, since none of these are outliers, we will depict a line from 7, which is the smallest data value to 65, which is the largest data value. Finally, we will add a box from our quartiles (\(Q_1 = xx\) and \(Q_3 = 40\)) and a line at the median of 31. All together nosotros have:
Of course, a software version volition await quite a bit better. Too note that boxplots can be drawn horizontally or vertically and you may run across either every bit you go on your studies. Equally an instance, here is the aforementioned boxplot done with R (a statistical software plan) instead:
Summary
Remember – pay attention to how these box plots are put together in order to practice a better chore at reading the data they provide. Since yous now know that middle line is the median, you can just look at the box plot and know that l% of the salaries were less than $31,000 or so. As yous can see, a box plot tin not only show you the overall pattern only too contains a lot of data nigh the data set. To see more nigh the information you can gather from a boxplot, see: How to read a boxplot
Subscribe to our Newsletter!
We are e'er posting new free lessons and adding more study guides, estimator guides, and problem packs.
Sign up to become occasional emails (once every couple or 3 weeks) letting you know what's new!
Source: https://www.mathbootcamps.com/how-to-make-a-boxplot-box-and-whiskers-plot-by-hand/