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7th Grade Math / Lesson 3: Box and Whisker Plots

BOX AND WHISKER PLOTS
What will we be learning in this lesson?


  • In this lesson you will learn how to make box and whisker plots to display data.
  • You will also interpret the meaning of what is represented by a box and whisker plot.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


Warm up problems
Check your answers


  1. Add up the numbers and then divide by how many you have.

  2. The number in the middle when you put the numbers in order.

  3. The number that occurs most often.

  4. Mean: 36.22
    Median: 35
    Mode: 35

  5. Median: 31.5


Box and Whisker Plot

  • To create a box and whisker plot you must be able to find the median of a set of data. Remember, median is the number in the middle. You must put the data in order before you determine which value is in the middle. What do you do if you have two numbers in the middle? Add them up and divide by two.

  • Once you find the median, you now have two groups of numbers, the upper half and the lower half.

  • With box and whisker plots, you will then need to find the median of each of those groups. The middle of the upper half is called the Upper Quartile. The middle of the lower half is called the Lower Quartile.

  • Once you find these other medians, you have now separated your numbers into 4 equal groups. You have numbers less than the Lower Quartile, between the Lower Quartile and the Median, between the Median and the Upper Quartile, and numbers greater than the Upper Quartile.

    • Let's use the following data values to begin making our box and whisker plot.
    45, 51, 49, 42, 54, 43, 50, 47
    Steps to follow:
    1.  Put data values in order.        42, 43, 45, 47, 49, 50, 51, 54
    2.  Find the range.              54 - 42 = 12
    3.  Find the median.              47 + 49 = 96 / 2 = 48
                                         so 42, 43, 45, and 47 are in the lower half and
                                                   49, 50, 51 and 54 are in the upper half
    4.  Find the lower quartile.      43 + 45 = 88 / 2 = 44
    5.  Find the upper quartile.      50 + 51 = 101 / 2 = 50.5
        so 42 and 43 are in the first group, 45 and 47 are in the second,    49 and 50 are in the third group, and 51 and 54 are in the last group.
                         *Notice that each group has the same number of data values in it.
    6.
    7.   (We will get to these)
    8.


    Let's look at what we have
    42, 43,44, 45, 47, 48, 49, 50, 50.5, 51, 54

    lower                median         upper
    quartile                                 quartile

    Now let's do steps 6, 7, 8
    6. Draw a number line appropriate for the range of values. Label all of the middle numbers that we found.


    7. Draw boxes above the number line from the quartiles to the median.


    8. Draw the whiskers from the quartiles to the end values.


    Those 8 steps will help you draw a box and whisker plot.

    And remember

    Each section of the box and whisker plot contains an EQUAL NUMBER OF DATA values, regardless of how big or small each section is.

    The longer the section is will only tell us that the data values are more spread out compared to the data values in the smaller sections.




    Answer the following questions
    1. What is the median?
    2. What is the lower quartile?
    3. What is the upper quartile?
    4. What is the range?
    5. There are more data values above 40 than there are from 20 to 25.




    Answer the following questions
    1. What is the median? 25
    2. What is the lower quartile? 20
    3. What is the upper quartile? 40
    4. What is the range? 50
    5. There are more data values above 40 than there are from 20 to 25.

    No, all sections contain the same number of data values regardless of the size of the section.


  • Can you create a box and whisker plot for a set of data?
  • Can you answer questions about the information given in a box and whisker plot?
  • Go back to the classroom to get to your homework and any other items you need to attend to.