Brief Description

By sixth grade, most students can calculate the Mean, Median, and the Mode, however; they do not really understand what these measures of central tendency are. They don’t have a realistic view of what to do with this new vocabulary or where this new math falls into place in their world.  This lesson is intended to make the measures of central tendency more applicable for them as well as to improve the students’ technology skills in Excel and toggling between screens.

Standards and Frameworks

Technology Standards

Academic Standards Objectives

Academic

Technological Pre-Requisite Technology Skills

It helps if kids have seen a spreadsheet before and used the Internet, however; pairing students with someone with Excel expertise will help.

Materials

Internet ready computers – at least 1 per 4 students and Microsoft Excel

Accommodations for Special Needs

When grouping students for this activity, put the stronger computer literate students with the novices.  Give gifted learners more challenges.  I modeled my lesson on a classroom computer and then left the information there so that 2 lower kids would have a head start.  For my autistic student, I set up the computer and taught him to toggle back and forth between screens.    Gifted learners can find new sites where the measures of central tendency can be applied – in doing this; they can apply the measures of central tendency to higher levels of usage.

Procedures

  1. Lesson 1 – teach the meaning of mean, median, mode, and range.  Use a textbook or the Internet: Below are two great sites that will help students understand the meaning and application of the central tendencies:
      2. http://www.zone101.com/LearningZone/MathZones/theory/grade6/meanmode.htm
      http://www.brainpop.com/
  2. Lesson 2 – Demonstrate how to use Excel.  Use a computer lab, and group students 2-4 per computer.  This way they can help each other to do this and no student will be left behind.   (The following is a step-by-step instruction for Excel – if you know how to use it go to #3.  You can also see the Excel example.)
      3. a.  Have students open up an Excel document and then, starting in A2, vertically type a list of given numbers; say, 12, 13, 15, 12, 15, 16, 18, 20, 12, 11, 13, 17, 19, 12. (See example)
      b. Now have students use the A-Z icon on the toolbar to arrange the numbers from least to greatest.  Be sure that you are in the A column before you click on the A-Z icon.
      c. Next ask them to estimate the mode; they should be able to see the number that appears the most. To check their answer, create a mode function.  In C2 type Mode.  In D2 click on the fx icon, select Mode as the function (you might have to look in the All category to find it).  Click on OK.  In the next window where it says number 1, highlight the range of numbers and click OK.
      d. Now, ask students to find the median – this is the number in the middle once the set has been arranged from least to greatest.
      e. In the case of this set of data and many others, there is an even number of items.  We can figure the Median by using an Excel function.
      f. Have them type the word Median in C3 and then click in D3.  Now they will click on the fx icon and select Median.
      g. Here they will be given choices of what formula they want.  They should choose average.
      h. Next, a window will appear – have the kids move it so they can see the numbers.  Click OK.
      i. Then they should highlight the range of numbers in the box next to Number 1.  Click OK.
      j. Now, have the students type the word Mean in C4, then click in D4.
      k. Now, again, click on the fx icon.  Ask for Average.  Click OK, move the box and highlight all of the data.  Click OK.
      l. The last statistic that needs to be entered is Range.  This is the most difficult because students need to create their own formula.  Type the word Range in C5 and click in D5.
      m. Now click on the = sign next to the formula bar and you will use the formula bar to type what you want the computer to do:
        i.  Click on the cell of the last data entry, A15 (in this example).  Click the minus sign – and then the cell of the first data entry, A2 (in this example).  Click OK.
        ii.  The biggest problem with this is if the kids reverse the highest and lowest number and then their result is a negative range.  If this occurs, just click on the answer and adjust the formula in the formula bar.
  3. Lesson 3: This lesson will help students to get used to having two screens open on the computer and they will learn to toggle back and forth between them. Have students access the Track Star http://trackstar.hprtec.org/main/track_frames.php3?track_id=78328&nocache=1548746914 and then proceed to use the Excel program to calculate the directions in the Excel document.  It doesn’t ask them to calculate range, however; knowing that this is on the Stanford 9 and many other assessments, it is essential that they practice this and understand the terminology. I have attached a directions document for the non-sports minded that will help to explain the Trackstar.
      4. a. Basically, to use trackstar, there are 3 things to know:
        i. The top yellow section is the directions
        ii. The left side yellow section gives the link to the website. Students will need to click all three links listed.
        iii. The actual website is in the center of the page.
  4. Lesson 4 Extension: Ask students to print out their Excel charts with their names on it.  They can talk about this as a class. Some of the data was misleading. For example, Cal Ripkin missed a season and his batting average was 0 so that made his range larger than it really should be.  You may also want to teach students how to do graphs with this data. Talk about the fact that when most of the data is made up of the same numbers, the mode is the best measure of central tendency – or the number that best describes the set.  When the range is large, the best measure of central tendency is the median.  It would best describe the set of data.  When the set of numbers is relatively close, then the mean is the best measure of central tendency.  It takes some higher-level understanding of the mean, median, mode and range to do this.
  5. The last lesson, the one that will let you know that your students really understand this is when you give students the class test scores and have then evaluate them with Excel using the measures of central tendency and range. Range is important and while it is not the best measure of data, it can let you know if there is a large gap.  Knowing this:
      6. a. First have your students type in their test or quiz scores from any given subject. Then have them apply all they learned about calculating in Excel.  Have them write in a Word document – hence having 2 documents open again. Ask the students to explain what measure of central tendency best describes their test scores and why.  Then ask them which is the worse descriptor and why. (This is a great assessment because it is applicable to life.)
        i. Example:
          1. Suppose my test scores were 80, 90, 88, 97, and 71. My average or mean is about 85, the mode is none and the median is 88. and the range is 26.  Because my range is so large, it says nothing about the data.  The mean and median are both very close and therefore very good descriptors of my grades.
Assessment

The student print outs will tell you if they were able to calculate the mean, median, mode and range, and also if they were able to toggle between screens.  Test academic knowledge by evaluating various sets of data using the measures of central tendency. Use the information in procedure #4 and #5 to evaluate higher levels of thinking. You can also use your monthly gas or electric bill to show other real life uses for the measures of central tendency.

Teacher Name: Niki Tilicki
Site: Wilson
Date Submitted: October 2, 2002