I.A.? Pining For Some Needles - Mean Median Mode

Teacher pages

Synopsis:

Students will have the opportunity to measure needles on pine trees to examine various measures of central tendency and to investigate differences and similarities between individuals and within populations. Data will be analyzed in a variety of ways, including the computation of mean, median and mode, and as a graphic representation indicating frequency distributions for particular sizes. (This works well with science and math team teaching)

Goals:

  1. Practice measuring physical characteristics of organisms in a natural setting.
  2. Analysis of data through mathematical/statistical procedures.
  3. Analysis of data through graphic representation.

Major Concepts:

Previous knowledge, skills, and experience needed:

Materials:

Directions:

  1. Divide the class into two large groups - each group will be responsible for one pine tree
    1. Divide the large groups into teams - 2 or 3 students per team.
    2. Assign each of the small teams a number of pine needles to measure (the combined total for all the teams in one large group should equal 100).
    3. Each team should appoint a recorder to record the measurements.
    4. Each team should be issued a metric ruler.
  2. Take the groups outside to a stand of pine trees (white pines are easy to use for this exercise - in any case, each tree needs to be of the same species).
    1. Assign each large group to one pine tree designated Pine Tree A or Pine Tree B
    2. Tell the teams that they will be measuring the length of the pine needles from the base of the branch to the tip of the needle (metric) WITHOUT removing or damaging the needles. Needles should be measured from various locations.
    3. Each team should measure the number of needles they have been assigned to measure and record the data on a sheet of paper
  3. Bring the groups back into the classroom and have the students write their measurements on the board. The measurements should be grouped by Tree A and Tree B with 100 measurements for each. Have the students record the measurements in their own notebooks.
  4. Have the students suggest ways to organize the data to describe the needle characteristics of each pine tree. (Possible ways to organize the data: ordered lengths, Venn diagram for comparison of tree A and B, frequency distribution for lengths or clusters of lengths, central tendency measures, range of lengths)
  5. If students do not suggest mean, median and mode, reintroduce the concepts (for instance, from Know Your Lemon) and have the teams use the collected data to compute the measures.
  6. Have each team of students construct a frequency distribution graph for the needle measures of each tree. Mark the mean, median and mode for each set of tree measures.
  7. Have students answer the following questions (can be done as a discussion or in individual teams)
    1. Were all the needles the same length? (1 point)
    2. Was the range of needle lengths the same for Tree A as for Tree B? (1 point)
    3. What are some human characteristics that might vary in the same way that needle lengths vary in pine trees? (2 points)
    4. Give two or three possible explanations for the differences in pine needles and for differences in humans. Are there any similarities between pine needles and humans in terms of the explanations? Do they relate to any of Maslow's Hierarchy of Needs? (5 points)
    5. Compare the frequency distribution graphs for the two trees. Was there much overlap between the needle length distributions? Were the measures of central tendency similar or different? (2 points)
    6. If you did the same measurements on a tree at the top of a mountain with an elevation of 2000 meters and compared it to your tree measurements from school, would you expect your answer to Question (e) to be the same? Why or why not? (schools at higher elevations might use a tree at sea level for a comparison) (3 points)
    7. Did you construct the graphs on the same page or on different pages? Describe one advantage AND one disadvantage for having the graphs on the same page. (2 points)

Student Product: (per team)

I.A.? Pining For Some Needles - Mean Median Mode

Student pages

Fill in the chart below as the information is given to you:

Tree Assignment: A or B

Number of Needles to Measure: ___________

Needle measurements:
Your Measures: _____________________________________________________________

_____________________________________________________________

Rest of the class:










Mean: _______ Median: _______ Mode: _______

Other tree A or B (information from the board):

Needle Measurements:




Mean: _______ Median: _______ Mode: _______

Questions:

  1. Were all the needles the same length? (1 point)


  2. Was the range of needle lengths the same for Tree A as for Tree B? (1 point)


  3. What are some human characteristics that might vary in the same way that needle lengths vary in pine trees? (2 points)


  4. Give two or three possible explanations for the differences in pine needles and for differences in humans. Are there any similarities between pine needles and humans in terms of the explanations? Do they relate to any of Maslow's Hierarchy of Needs? (5 points





  5. Compare the frequency distribution graphs for the two trees. Was there much overlap between the needle length distributions? Were the measures of central tendency similar or different? (2 points)


  6. If you did the same measurements on a tree at the top of a mountain with an elevation of 2000 meters and compared it to your tree measurements from school, would you expect your answer to Question (e) to be the same? Why or why not? (schools at higher elevations might use a tree at sea level for a comparison
    (3 points)




  7. Did you construct the graphs on the same page or on different pages? Describe one advantage AND one disadvantage for having the graphs on the same page.
    (2 points)


(THIS IS A HOLDOVER FROM THE PREVIOUS RTFTOHTML TRANSLATION SCHEME, BUT IÍM LEAVING IT IN JUST FOR REFERENCE --GAF)FOLLOWING IS HIDDEN TEXT THAT LOADS THE IMAGES ON THE WEB PAGE TO LINK EACH ACTIVITY PAGE TO THE PREVIOUS AND NEXT ACTIVITIES AND BACK TO THE MODULE. THE MODULE, UNIT, AND ACTIVITY NUMBERS [IN THESE BRACKETS] MOST BE MODIFIED TO PROPERLY LINK. NO BACKLWARD LINK IS NEEDED FOR THE FIRST ACTIVITY; NO FORWARD LINK IS NEEDED FOR THE LAST.