Box-and-Whisker Plot. You know I like my visuals. I don't come from Missouri but, when it comes to math, I need you to show me. 😉 (You see what I did there?) Box-and-whisker plots (box plots) are cool because they show you characteristics of the data you're working with that may be very useful to you. You can definitely see whether or not the data set is skewed. Also, you may be able to tell what the distribution of the data is. These days, software is used to create boxplots by those who need to use such information. Once a data set isn't too crazy, doing a box plot by hand isn't too bad. So, that's what we'll be doing this week.
To solve this week's problem in completion, you need to recall the following math skills:
✔️ How to find the five-number summary of a data set
✔️ How to construct a box plot
Here is what WMP! #56 says...
Check back on Friday, September 24th for the solution, which will be posted below ⬇️.
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✏️📓 Solution Time! 📓✏️
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Are you ready? I think I am so...let's go! I think a good way to tackle this problem is to outline steps to take.
Step 1. Order the values from least to greatest.
It's super important to put your data ascending order. If not, then the values in the five-number summary will be incorrect.
Now that the data has been put in order, we can get the five-number summary needed to help us produce the boxplot.
Step 2. Identify the extreme values.
The extreme values are two of the five numbers needed to construct the boxplot. These values are the minimum and maximum values and they are used to make sure the whiskers are the right length. Since the data set is in order, those values are on either end of it.
Step 3. Find the median.
The median is the middle number in an ordered data set and is the third number we're finding in the data set. This data set has twenty values in it, which means there are two numbers in the middle. When this happens, the median is computed by taking the average of the two middle numbers. (The median is also known as the second quartile, Q2)
Step 4. Find the first and third quartiles.
The remaining two numbers part of the five-number summary are the first and third quartiles, Q1 and Q3 respectively. To find these, the ordered data set needs to be broken into two subsets--the lower half and the upper half. Since the data set has twenty values in it, the lower and upper halves will have 10 values each.
Q1 is the median of the lower half, while Q3 is the median of the upper half.
Step 5. Construct the box plot.
Time to draw! We've found all the numbers part of the five-number summary and here they are listed in ascending order:
Minimum = 32
Q1 = 56
Median = 74.5
Q3 = 82.5
Maximum = 99
We'll construct an appropriate timeline for the plot, place a marker at the appropriate places over the number line, then draw the whiskers and box.
...And there you have it--a box plot for the test scores data set we worked with!
(I checked my work using Microsoft Excel and Google Sheets but kept getting a different value for Q3. 🤷🏿♀️ Not sure why. Share any insights you have. I checked to see if I had any errors in my work. Not sure if I missed any errors I may have. 🤷🏿♀️)
▪️ Did you get the same values for the five-number summary??
▪️ Did you use technology to check your work??
▪️ Let me know what you thought about this week's problem in the comments section.
Thanks for solving with me this week!
On to WMP! #57. 🤸🏿♂️
Cheers!
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