Weekly Math Problem #56

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...

Happy solving!

Check back on Friday, September 24th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 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!

The Younge Lady

Weekly Math Problem! #12

Solving A STATISTICS Word Problem. One of my favorite sections of math is stats! 😍 I really like it because it was the first time I really noticed math that I learned in school all around me--in advertisements, commercials, in education, in finance, in the medical field, pharmaceuticals, etc. This is one area in mathematics that I want to be so much more comfortable with and better at. I have a few books that I've purchased over the years from the time I first started learning and understanding stats in undergrad until now. Two of those titles include The Humongous Book of Statistics Problems by W. M. Kelley and R. A. Donnelly Jr., and Statistics in a Nutshell, Second Edition by Sarah Boslaugh. Of course there are also electronic textbooks and stats PDF files in my possession. **Does anyone else scour the internet for PDF files? 👀 Asking for a friend. 😅** Also, because I tutor statistics, I make sure to have resources on hand to refer to, so that the people I work with get the best help they can get from me. I have also purchased and read Numbers Rule Your World by Kaiser Fung. I need to read this book again. I enjoyed it the first time I read it and definitely wouldn't mind reading it again.

Even though I really like statistics, word problems can definitely be annoying. If you're like me, you need to read word problems at least three times before feeling comfortable enough to start solving. 

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Working with normally distributed data

    ✔️  Working with "small" sample sizes

    ✔️  How to conduct a t-test

    ✔️  Hypothesis testing 

    

Here is WMP! #12...

Happy solving! 

Check back on Friday, July 24th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I'm working with some students this summer and after their review of pertinent information concerning methods to solve specific types of word problems, they freely expressed how much word problems gave them a problem. I totally get it. Word problems definitely make me sigh quite a few times while reading them. So, I decided to color-code this week's word problem with the information and formula used to come to the appropriate conclusion.

**The critical value above came from this t-table.

GeoGebra Classic  has a cool probability tool that shows you the graph of some discrete and continuous probability distributions. It also generates some statistical results of a few different types of statistical tests that are typical when learning statistics. (I encourage you to check it out.) Here are the graph and results of the t-distribution with information from the word problem:

◾️ How do you feel about statistics?? 

◾️ Were there any differences between how you solved the word problem and what I presented above?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

See you next week for...WMP! #13 👩🏿‍🏫

Cheers!

The Younge Lady