Name: Michelle Diamond
Title: Mean, Median, Mode
Grade level: 3
Statistics are a measure of a sample from
some populations or other types of data. They
are measures of data that quantify some attributes of specific numbers. The
things that are most often described numerically about a set of data are the
distance between the highest and lowest data values (range), some measure of
the center (average), and how the data is dispersed within the range (variance
or dispersion). Elementary children can explore the importance of these
statistics by doing so informally.
The mean, median, and the mode are specific
types of averages or measures of central tendency. Other averages exist as well
but these are the ones that are taught at the elementary level.
The mode is the value that occurs most
frequently in the set of data. Mode is not greatly influenced by extreme cases
but is probably the least important or least used of the three types.
The mean is computed by adding all of the
numbers in the set and dividing the sum by the elements added. This is usually
referred to as the average although the terms are not synonymous. The
arithmetic mean is the most frequently used measure of central tendency. It is
generally reliable, easy to use, and is more stable than the median.
The median is the middle value in an
ordered set of data. Half of the values lie at or above the median and half
below. It is a set of numbers arranged in ascending or descending order. The
middle number is the median. In the event that there are two middle numbers, the mean of the two will be considered the median.
Standard 1: Number
Systems
Benchmarks
1.1 Add, subtract, multiply and divide whole
numbers, and investigate inverse relationships with and without calculators.
1.3 Estimate,
approximate, round off, or use exact numbers, as appropriate, in calculations.
1.7 Describe and
compare quantities by using whole numbers, decimals, and fractions.
Standard 5: Using
Data, Statistics, and Probability
Benchmarks
5.5 Solve problems
using various strategies for making combinations.
5.7 Interpret data
using the concepts of largest, smallest, most often, and middle.
Student
Materials:
Teacher
Materials
·
Boards w/
definitions and examples
·
Data Sheets
·
MMM Homework
Assignment
·
MMM Rap
Anticipatory set: at tables
Lab: at tables
Closure: at tables
Anticipatory set: whole class
Lab: individual
Closure: whole
class
Step By Step
a) Tell the students that today we are going
to learn how to measure sets of data that are called statistics. High school
kids do this kind of math. I think you guys are so smart that I think you will be able to do it in the third grade.
b) I will ask the students if they know how to
figure out batting averages or basketball shooting accuracy. (S- may say add
them together) Suppose Michael Jordan get 25 pts on Thurs, 23 pts on Fri, and
27 pts on Sat. Can anyone tell me what MJ’s point average is? (S- No)He would have an average of 25 pts
per game even though on Sat he got 27 pts. I am going to teach you all how to
figure out how to find the mean or average.
c) I will ask the students what temperature
occurred most this week [45, 55, 40, 50, 55] (S- 55). I will explain to the
students that this is what we call the mode of a set of data.
d) I will choose 6 students and a Temple
Teacher to stand in the front of the room in a straight line. The Temple
teacher will stand in the middle while on either side of her the student
heights will gradually lessen Example Then I will ask the class who is in the middle? (S- Ms.
K) I will ask how they know she is in the middle. (S- There are three kids on
each side of her. I will tell the class that this is what it means to find the
median.
e) 
I will explain that all these pieces of
information are called data that describe a piece or part of something bigger.
f) Tell students we are going to find the
mean, median and mode of different sets of numbers. Say the best part about
learning how to do this is that you will be able to help an older
brother/sister/cousin learn how to do this and you guys are not even in high
school. Now we are going to sing a rap to help us remember the mean, median,
and mode.
g) To help the students remember each term we will sing a little Rap together to help them remember.
Rap- MMM Rap
The MMM Rap
The MMM Rap
Mode is the # you see the
most!
I said Mode is the # you see
the most.
The MMM Rap
Median is the middle man
Just line up the #’s as best
as you can
From smallest to largest
Yeah yeah
Median is the middle man
The MMM Rap
Now Mean Mean he is the best
Of course he is better than
all the rest!
Just add up the #’s
And then divide
When you‘re done
You have only one!
The MMM Rap
When you rap – it’s all just
a snap!
Approximate
time 5- 10 minutes
I.
I will
explain to the students the activity we are about to do. First, we are going to
do two different types of problems together to figure out how to find the mean,
median, and mode. Then after we have done this you will need to do an activity
on your own to find the mean, median, and mode.
a) I will give two examples of the mean and
have the students work through each example with me.
1) (Show example on the overhead.) Kym has a
4, 4, 4, 2, 1 for test scores. We want to find out the mean or average amount
of her test scores.
2) Class, what do you think we should do to find out? (S- Add them)
3) Lets add them. 4+4+4+2+1=15 After adding them
we get 15 pts. That # just tells us the total # of points for all of the tests.
4) To find the average or mean, after we add
the #’s together we need to divide by # of numbers we added together. We added
4, 4, 4,2,1. That is 5 numbers. So we need to take the total # of the tests
(15) and divide that by 5. 15 ) 5= 3.
5) The average or mean of Kym’s test scores is
a 3. Even though Kym got a few 4’s on her tests, she had two lower scores and
when you average them all together the low scores come up and the high scores
go down and they all kind of meet somewhere in between.
6) Let’s try another one to make sure we all
understand how to find the mean or average of a set of data.
7) We will use a weather forecast. The
temperatures are [ 10,12,13,15,10]. These are the temperatures for a very cold
week in Jan. We want to find the
average or mean temp for the week.
8) Who can tell me what we do first? (S-Add)
(Add the numbers together on the overhead) 10+12+13+15+10=60
9) We added all the numbers, now what is the
next step? (S- divide) How do we know what # to divide by? (S- as many #’s as
we added) 10,12,13,15,10 are the numbers added and there are 5 of them.
Therefore, we divide by 5. 60 ) 5= 12
10) What is the average temperature of the
week? (S- average or mean is 12). The mean or average temperature is 12
degrees.
11) I want everyone to repeat the part of the
rap that relates to the mean. (S- repeat section)
12) Great job everyone.
b) I will give two examples of the median and
have the students work through each example with me.
1) Now we are going to use a set of data to
find the median of a set of #’s. Can anyone remember from the rap we sang, what
the median is? (S- middle man) That’s right!
2) Lets look back at Kym’s test scores. (On
the overhead) [4, 4, 4,2,1.]
1) Boys and girls, we do not want to know which test had the
highest score or the lowest score. What do we want to know when we are trying
to find the median? (S- the middle number) Yes!
2) The first thing we need to do is to put the
numbers in order from smallest to largest. What number is the smallest? (S- 1
)Then what number comes next? (S-2)Good. What is the largest number? (S- 4 )
3) Now that the numbers are in order, how
would we find out which one was in the middle? (S- Look at them) (Demonstrate
how to start at each end by putting fingers on the first and last numbers in
the row and move your fingers inward until getting to the center #.) What # did
both of our fingers land on? (S- 4)
Yes, that right. In this set of data, the median is 4.
4) Let’s try another one to make sure we all understand
how to find the median of a set of data
5) We will go back to the weather forecast. I
have a set of numbers [10,12,13,15,10]. We want to find the median of these
numbers.
6) What should we do first? (S- Put them in
order)
7) What kind of order? (S- smallest to
largest) 10,12,13,15,10.
8) What do we do next? (S- use our fingers to
find the middle one)
9) Who can tell me what number is the
median? (S-12Very good!
10) In this set of data, the median is 12.
11) I want everyone to repeat the part of the
rap that relates to the median.(S- repeat section)
c) I will give two examples of the mode and
have the students work through each example with me.
1) Now we are going to use a set of data to
find the mode of a set of #’s. Can anyone remember from the rap we sang, what
the mode is? (S- the one you see the most) That’s right!
2) Look at this set of #’s [4, 4, 4,2,1] These numbers are Kym’s test
scores.
3) How would we find out what the mode is? (S-
look to see what number you see the most) Yes, that’s right.
4) Sometimes there are to many numbers to look
at so what do you think we should do first? (S-put the #’s in order) Yes, that
would help us to see what number shows up the most.
5) Who can tell me what order the numbers
should go in? (S- 1,2,4,4,4) Good
6) What number do you see the most? (S-4)
That’s right. In this set of data, the mode is 4.
7) I want everyone to repeat the part of the
rap that relates to the mode.(S- repeat section)
d) Who can tell me if we were looking for the
mean in a set of data what we would do? (S- add then divide) If I was looking
for the median in a set of data what would I do? (S- put them in order and find
the one in the middle) If I was looking for the mode of a set of data what
would I do? (S- look for the one you see the most)
Approximate time
20 minutes
II.
Now we are
going to do another activity where you will need to find the mean, median and
the mode of a bag of M&M’s. The reason I want you to do this is that I just
put a handful of M&M’s in each bag. I want to see if everyone gets equal
numbers of each colored candy. You need to follow all the rules or you will not
be able to participate.
1) Each student will get a bag of M&M’s
and an M&M worksheet.
2) Directions- Do not eat any of the candy
until we are done.
3) First, you will open the bag and sort the
candy by colors. You will count the candy and write the # of each color in the
table on the work sheet.
4) Using the numbers in the table, you will
find the mean or average of all the candies.
5) You will then find the median.
6) Lastly, you will find the mode.
a) I will now past out the materials. Please
do not touch anything until you are told to.
b) Open the M&M’s and sort them into
colors. Then stop and look at Mrs. Diamond. This way I will know you are ready
to move on.
c) Now count each color and write the number
in the table on the worksheet. Put the candy back in the bag. Then stop and
look at Mrs. Diamond.
d) Now we want to find the mean of all the
M&M’s. I want to see if the M&M in the
middle has the same number of pieces for the entire class. Who remembers what
we do? (S- add then divide) Good. Now everyone should find the mean or average
of the M&M’s. Then stop and look at Mrs. Diamond.
e) Now we want to find median. Who remembers
what we do? (S- put them in order and find the one in the middle) Find the
median. Then stop and look at Mrs. Diamond.
f) Now
we want to find mode. Who remembers what we do? (S- look for the one you see
the most) Find the median. Then stop and look at Mrs. Diamond.
g) We have now found the mean, the median and
the mode of each bag of M&M’s.
h) What was the average # of M&M’s?
(S- )
i) What was the median # of M&M’s?
(S- )
j) What was the mode of the M&M’s?
(S- )
k) Since we all had the same answers to all of
the questions do you think Mrs. Diamond really just put a hand full in or did I
count them out? (S- you counted them)
Approximate time
10-15 minutes
I will have the students sing
the rap again. Then after, I will ask the students what we have just learned.
What does it mean to say the mean median and mode. The students will each have
a set of three index cards. Each card will have one word written on it (mean,
median, and mode). I will tell the
students that I am going to ask them a question and they each need to answer by
holding up the correct card. Say, I am going to look at a set of numbers and
see which occurs most often. (There will be a visual on the overhead while
asking these questions.) What am I trying to find? (S-hold up the mode card) Next, I am
going to add up all the numbers and divide. What am I trying to find? (S- hold
up the mean card). Lastly, I am going to put the numbers in order and find the
middle value. What am I trying to find? (S- hold up the median card). I will
then have the students sing the rap to conclude the lesson.
Approximate time 5
– 10 minutes
This would be an activity where the
students would be able to collect data on the birthdays of each student in the
class to find the mean, median, and mode. First, the student would have to find
out in what month each student was born. (Jan, Feb, Mar, etc.)
After collecting
the data the students would have to decide how to arrange the data so that they
can find the mean, median, and mode of those numbers.
Example: Jan-#,
Feb-#, Mar-# and so on. Then the students would add the numbers together and
divide to find the mean or average # of birthdays each month. The students
would then need to put the numbers in order to find the median, to see which
month is the middle of all the birthday months. Finding the mode would follow
this, which month has the most birthdays.
The students could
also make suggestions.
The students will be required
to participate in all activities. The students will be required to complete
assigned class work and homework. This will be graded.
Short Term Assessment:
As the students are participating in the activity, the teacher will be going
around to each student with a checklist to assess each part of the lesson.
The teacher will
be looking to see if the students are sorting, recording data, and apply the new
methods for finding the mean, median, and mode. The teacher will also assess
the students at the conclusion if the lesson. The students will each have a set
of three index cards. Each card will have one word written on it (mean, median,
and mode). I will tell the students
that I am going to ask them a question and they each need to answer by holding
up the correct card. Say, I am going to look at a set of numbers and see which
occurs most often. (There will be a visual on the overhead while asking these
questions.) What am I trying to find? (S-hold up the mode card) Next, I am
going to add up all the numbers and divide. What am I trying to find? (S- hold
up the mean card). Lastly, I am going to put the numbers in order and find the
middle value. What am I trying to find? (S- hold up the median card) This will
show the teacher if all students understand the methods of the topic.
Intermediate
Assessment: The students will receive a homework assignment that will let the
teacher know if all students meet the objectives of the lesson. The assignment
will include problems that require students to find the mean, median and mode.
There will also be a matching section which will require the students to match
each word with the steps used in finding the answer for mean, median, and mode.
See attached
Long Term
Assessment: There will be questions on an end of unit exam to reassess the
material taught in the lesson. The students will be give a set of numerical
data and will be required to find the mean, median, and mode for each set of
data. An example of a test questions would be:
John
has 4 friends at school, 11 friends at basketball, 8 friends in his
neighborhood, and 9 friends at church. What is the mean or average number of
friends that John has?
I
have 6 books about dinosaurs, 10 books about dogs, and 2 books about playing
basketball. Find the median of this set of data.
I
have a bunch of quarters in piles. Pile one has 4 quarters, pile two has 6
quarters, pile three has 4 quarters, and pile four has 5 quarters. Using the
information about the piles, Find the mode.
Students will be given a handout to
complete. The handout will contain mathematical problems involving various
number set in which the students will be require to find the mean, median, and
mode.
·
MMM Rap
·
MMM worksheet
·
Mean – Median
– Mode Homework
Bobrow, Jerry, Math Review for Standardized Tests
Nebraska, 1985
Cutler, Penelope
Gallagher, Pam
Langley, Russell, Practical Statistics New York, 1971
Triveri, Lawrence
A., Fundamental Concepts of Elementary
Mathematics New York, 1977
Van de Walle, John
A., Elementary and Middle School
Mathematics. 2nd Ed. New York,
1998
Attachments
MMM Rap
The MMM Rap
The MMM Rap
Mode is the # you see the
most!
I said Mode is the # you see
the most.
The MMM Rap
Median is the middle man
Just line up the #’s as best
as you can
From smallest to largest
Yeah yeah
Median is the middle man
The MMM Rap
Now Mean Mean he is the best
Of course he is better than
all the rest!
Just add up the #’s
And then divide
When you‘re done
You have only one!
The MMM Rap
When you rap – it’s all just
a snap!
** Kym’s Test Scores **
4 2 4 1 4
First
Add Then Divide
) =
Total Mean
Order
Small to Large
Median
The one you see most often
Mode
** Weather Forecast **
10º 12º 13º 15º 10º
First
Add Then Divide
) =
Total Mean
Order
Small to Large
Median
The one you see most often
Mode
Kym’s Test Scores
|
Weather Forecast
|
||||||||
|
4 |
2 |
4 |
1 |
4 |
Mon |
Tues |
Wed |
Thurs |
Fri |
|
10˚ |
12˚ |
13˚ |
15˚ |
10˚ |
|||||
|
1. Mean_______ |
2.
Mean_______ |
||||||||
|
3. ____ ____
____ ____ ____
Median______ |
4. ____ ____
____ ____ ____ Median______ |
||||||||
|
5. ____ ____
____ ____ ____
Mode______ |
6. ____ ____
____ ____ ____
Mode______ |
||||||||
M & M Worksheet
Name _______________ Date________________
Write the
number amount of each color of M & M’s in your bag in the table below.
|
Red |
Yellow |
Green |
Orange |
Brown |
|
|
|
|
|
|
|
Find the mean.
Mean _________ |
|
Find the median. ______ _______
_______ _______ _______
Median _______ |
|
Find the mode. Mode
_______ |
Name
__________________ Date
______________
MMM
Homework
Directions:
Find the mean for each set of numbers.
Show all work.
To find the mean of a group
of numbers:
Directions: Find the mode
for each set of numbers. Show all work.
To find the mode of a group
of numbers:
·
Arrange
the numbers in order by size. Smallest to largest.
·
The one
you see repeated the most is the mode.
|
7.
[
2, 8, 5, 6, 2, 5, 9, 4, 5 ]
___ ___ ___
___ ___ ___
___ ___ ___ mode________ |
|
8.
[
10, 9, 2, 10, 6, 4, 10, 2, 9 ] ___
___ ___ ___
___ ___ ___
___ ___ mode________ |
Find the median for each
set of numbers. Show all work.
To find the median of a group
of numbers:
·
Arrange
the numbers in order by size
·
The median
is the middle number.
|
9.
[
11, 21, 12, 17, 36 ]
_____ _____ _____
_____ _____ median________ |
|
10.
[
43, 51, 26, 38, 27 ] _____
_____ _____ _____
_____ median________ |
