**Lesson Plan I**

by: Chris Povich

Macintosh Clarisworks Users: download the original lesson in Clarisworks 4.0 or higher.

**Topic:** Introduction to
Descriptive Statistics with Mode, Median, Mean, and Range.

**Grade Level:** Six through ninth grade.

**NCTM Standards:** 2-3 Express mathematical ideas
orally and in writing.

10-3 Understand and apply measures of central tendency,
variability, and correlation.

**Day One**

Activity One: Students will work in groups of three and four
members. Each group will visit the URL, http://www.mste.uiuc.edu/hill/dstat/dstatintro.html,
and access, "Descriptive Statistics (Introduction to Mode,
Median, and Mean)," by Jay Hill. The groups will access the
pages dealing with mode, median, mean, and range.

Activity Two: Students will perform the dice game described by
Jay Hill in their groups.

Part A) Each group member picks two numbers ranging from one to
six. Students within the same group cannot pick the same two
numbers. Students within each group take turns rolling a
six-sided die fifty times. Each time a number comes up that
matches one of a student's chosen numbers, that student receives
a point. Students then are to make a bar graph on Claris Works
that represents their group outcomes.

Example of a Group's Outcomes:

Activity Two: Jay Hill's Descriptive Statistics Activity.

Part B) The class will now pool all their scores together. Each
group will put the class scores in order from lowest to highest.
Each group will create a bar graph of the class data on Claris
Works.

Example of Class Bar Graph:

Part C) Each group is to find the mode, median, mean, and range
for the class results. Then the groups will discuss which central
tendency best represents the scores of the class.

**Assessment: **Groups will turn in their histograms
and results at the end of the period for a group grade.

**Day Two**

Activity One: "What's Your Average"

- The teacher will write out questions which relate to a
unit or chapter being taught in another subject on index
cards. The teacher will then tape the cards on the back
of students in the classroom. (Students may not look at
the card on their back.)

- Students will then go to eight other students and ask
them to answer the question on their back using a number.
They must also ask for a one word clue to help them
figure out what their question might be. Students will
record this information on their paper.

- After soliciting the numbers and clue words, students
return to their desks/tables and find the average of the
numbers and attempt to write what the question is on
their backs from the given data.

- Each student will share their clue numbers, clue words,
average, and suggested question with the class. Then the
student will remove the question from their back so they
can compare the suggested question with the actual
question. Students are to answer if the numbers and/or
average helped them figure their question out. They will
also discuss with the class what the actual answer is.
Furthermore, students will explain if the high and low
scores were thrown out would their average be closer to
the actual answer.

Example Question:

How many bone are in the human body?

Answers:

200 Vertebrae

500 Skeleton

260 Cast

256 Calcium

200 X-ray

100 Connections

206 Broken

200 Skull

Average: 240.25 (Actual answer is 206. If the high and low scores
were thrown out, the average would then be 220.33. This is closer
to the actual answer.)

Activity Two: "Water on a Penny"

Part A) Each group will get an eye dropper, a glass of water, and
a penny. Each student in the group will make an estimate of how
many drops of water they will be able to put on the penny. Each
student in the group will take a turn and try to put as many
drops as they can on the penny. Students will post their results
on the board using a stem and leaf diagram. Each group is
responsible for copying the diagram down.

Example of Class Stem and Leaf Diagram:

Prediction Leaf Stem Results Leaf

3,5,3,6,5,4,7 0 3,5,2,4 1 0,7,2 2 6,9 6,5 3
4,2,1,0,6,4,9,9,6,7,8,4,5 0,8 4 0,0,1,2,1,2 0 5 5 6 7 Part B)
Each group will then use the TI-82 to come up with box plots for
the prediction data and the results data. The groups will then
sketch the box plots using Claris Works.

Example of Box Plots:

Part C) Students will attach the previous data in their journals.
They are required to discuss in their groups and write in their
journals about the mode, median, mean, and range for each set of
data. They are to discuss why the ranges are different and what
contributes to this.

**Assessment:** Students will turn in their journals
for a journal grade at the end of the week.

**Day Three**

Activity One: Review Using "Open Eyes" Project

Part A) Each student in the group will get a stop watch. The
student will close their eyes and start the stop watch. After
they think a minute has passed they will stop the stop watch and
open their eyes. The students in the class will pull their data
together and create a stem and leaf diagram, histogram, and a box
plot. Lastly, the students will discuss the mode, median, mean,
and the range of their data.

Example of Stem and Leaf Diagram in Seconds:

Stem Leaf

3 4, 4 5,0,5,3, 5 0 6 5,9,4,8,2,5,6,8 7 0,5,3,1,7,

8 1

Example of Histogram:

Example of Box Plot:

The mode = 45, 65, 68 seconds.

The median = 65.5 seconds.

The mean = 61.55 seconds.

The range = 81-34 = 47 seconds.

Part B) Students are to discuss about the range and if most of
the class estimated under or over a minute. How does the
different graphical presentations demonstrate this? How does the
different central tendencies demonstrate the estimations of the
class. (This discussion can lead into variance and standard
deviation.)

Activity Two: "Finger Snap" Quiz

Part A) Students will predict how many times they can snap their
fingers in thirty seconds. The class data will be collected and
listed in a chart on the board or overhead.

Part B) The teacher will run a stop watch for thirty seconds as
students snap their fingers. After thirty seconds the teacher
will collect and list the class results in another chart on the
board or overhead.

Part C) Quiz - The students individually are to produce a stem
and leaf diagram, histogram, and box plots for the given data.
Students will then write about the advantages and disadvantages
of each graphical representation. Then they will calculate the
mode, median, mean, and range for each set of data. They are to
choose a central tendency that best represents each set of data
and explain why they chose these particular measurements. The
ranges of the two data sets are to be compared and the students
are to explain why or why not there is a variation in the ranges.

**Assessment:** The "Finger Snap" Quiz
will be turned in and count as an individual quiz grade for each
student.