Welcome to IRSC’s LIVE Virtual Lesson on:

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Transcript Welcome to IRSC’s LIVE Virtual Lesson on:

Welcome to IRSC’s
LIVE Virtual Lesson
on:
Mean, Median, Mode,
and Range
Instructor: Mrs. DiMartino
How to participate in this
session:
What you will learn today:
How to define and compute:
a) the mean
b) the median
c) the mode
d) the range… of a set of data.
Why learn these skills?
We use statistics such as the mean,
median, mode, and range to
obtain information about a
population (group) from our
sample set of observed values
(data).
Mean
The mean is the “average” of
a set of numbers.
How to find the mean?
1. Add up all the numbers.
2. Then, divide by how many numbers
there are.
In other words, it is the sum divided
by the count.
Example 1: Finding the Mean
What is the mean of these numbers?
6, 11, 7
1. Add the numbers:
6 + 11 + 7 = 24
2. Divide by how many numbers there are (3):
24 / 3 = 8
The Mean is: 8
Example 2: Finding the Mean
What is the mean of these numbers?
94, 88, 100, 65, 89, 70
1. Add the numbers:
94 + 88 + 100 + 65 + 89 + 70= 506
2. Divide by how many numbers there are (6):
506 / 6 = 84.3
The mean is : 84.3
Example 3: Finding the Mean
What is the mean of these numbers?
$24.00, $16.00, $ 18.00, $34.00
1. Add the numbers.
$24.00 + $16.00 +$ 18.00 + $34.00 = $92.00
2. Divide the total by how many there are.
$92.00/4 = $23.00
The mean is: 23
Median
The median is the
"middle number"
in a list of numbers that
have been sorted by
value.
How to find the median?
1. Place the numbers you are given in
value order.
2. Find the middle number.
Example 1: Finding the
Median
Find the median of:
{ 6, 3, 7, 9, 4}
1. Place the numbers you are given in value order.
{ 3, 4, 6, 7, 9}
2. Find the middle number.
{ 3, 4, 6, 7, 9}
The median is : 6
Example 2: Finding the
median
Find the median of:
{ 12, 2, 6, 9, 7, 8}
1. Place the numbers you are given in value
order.
{ 2, 6, 7, 8, 9, 12}
2. Find the middle number.
{ 2, 6, 7, 8, 9, 12}
Wait a minute! There isn’t a middle
number!!!
Median (Ex:2 continued)
When there are two numbers in the middle…
1. Locate the two middle numbers. (7 and 8)
2. Add them together.
8 + 7 = 15
3. Divide that number by 2.
The median is : 7 ½
15 / 2 = 7 ½
Example 3: Finding the
Median
Find the median of:
{4, 9, 5, 13, 7}
1. Place the numbers you are given in value
order.
{4, 5, 7, 9, 13}
2. Find the middle number.
{4, 5, 7, 9, 13}
The median is : 7
Mode
The mode is simply
the number that
appears
most often.
How to Find the Mode?
1. First, put the numbers in order.
2. Then count how many there are of
each number.
3. Find the most frequently occurring
number.
Example 1: Finding the Mode
Find the mode of these numbers:
{ 3, 6, 7, 8, 7, 3, 2, 7, 9}
1. First, put the numbers in order.
{ 2, 3, 3, 6, 7, 7, 7, 8, 9}
2. Then count how many there are of each
number. Which number occurred most
frequently? { 2, 3, 3, 6, 7, 7, 7, 8, 9}
The mode is: 7
Example 2: Finding the Mode
(when there is more than 1 mode)
Find the mode of these numbers:
{3, 3, 2, 3, 6, 4, 8, 6, 6, 4}
1. First, put the numbers in order.
{2, 3, 3, 3, 4, 4, 6, 6, 6, 8}
2. Then count how many there are of each number.
Which number occurred most frequently?
{2, 3, 3, 3, 4, 4, 6, 6, 6, 8}
The modes are: 3 and 6
Example 3: Finding the Mode
Find the mode of these numbers:
{12, 9, 11, 6, 4, 3, 12, 8, 9, 12 }
1. First, put the numbers in order.
{3, 4, 6, 8, 9, 9, 11, 12, 12, 12 }
2. Then count how many there are of each number.
Which number occurred most frequently?
{3, 4, 6, 8, 9, 9, 11, 12, 12, 12 }
The mode is: 12
Range
The "range" is the
difference between
the largest and smallest
values (numbers)
of a set.
How to find the range?
1. First, put the numbers in order.
2. Locate the largest number and the
smallest number.
3. Then subtract them to find the
range.
Example 1: Finding the Range
Find the range of this set of numbers:
{4, 2, 6, 9, 7, 15, 3, 5, 6}
1. First, put the numbers in order.
{ 2, 3, 4, 5, 6, 6, 9, 7, 15 }
2. Locate the largest number and the smallest
number.
15 and 2
3. Then subtract them to find the range. 15-2 = 13
Example 2: Finding the
range
Find the range of this set of numbers:
{22, 16, 17, 8, 12 }
1. First, put the numbers in order.
{8, 12, 16, 17, 22 }
2. Locate the largest number and the smallest
number.
22 and 8
3. Then subtract them to find the range. 22-8 = 14
Example 3: Finding the
Range
Find the range of this set of numbers:
{1, 3, 9, 4, 20, 6 }
1. First, put the numbers in order.
{1, 3, 4, 6, 9, 20}
2. Locate the largest number and the smallest
number.
20 and 1
3. Then subtract them to find the range. 20-1 = 19
Word Problem Practice
A marathon race was completed by 5 runners.
What is the range of times given in hours below?
2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr
Solution:
1. Order the data from least to greatest.
2.7, 3.5, 4.9, 5.1, 8.3
2. Subtract the highest and lowest.
8.3 hr - 2.7 hr = 5.6 hr
Answer: The range of times is 5.6 hrs.
Word Problem Practice
On a frigid, winter day in February, the
temperature for 8 cities in Maine was recorded.
What is the mode of these temperatures?
-8, 0, -3, 4, 12, 0, -1, 0
Solution:
1. Order the data from least to greatest.
-8, -3, -1, 0, 0, 0, 4, 12
2. Count how many there are of each number.
Then, find the most frequently occurring number.
-8, -3, -1, 0, 0, 0, 4, 12
Answer: The mode of these temperatures is 0.
Word Problem Practice
In the first 9 weeks of school, Sarah’s test
scores in math were: 94%, 88%, 89%, 78%,
and 100%. What is her test average (mean)?
Solution:
1. Order the data from least to greatest.
78%, 88%, 89%, 94%, and 100%
2. Add the numbers.
78% + 88% + 89% + 94% + 100% = 449
3. Divide the total by how many there are (5).
449 / 5 = 89.8%
Answer: The mean is 89.8%
Word Problem Practice
Jimmy's phone calls lasted 20 min., 7 min., 9 min.,
12 min., and 8 min. He took data to show how long
his phone calls typically were. Find the median
value of his set of data.
Solution:
1. Order the data from least to greatest.
7 min., 8min., 9 min., 12 min., and, 20 min.
2. Find the middle number.
7 min., 8min., 9 min., 12 min., and, 20 min.
The median is :
9 min.
Any Questions?
Type your questions in the chat
window please for whiteboard
practice.
Print your participant
Window.
• Why? To email to your instructor as proof of
attendance. To get 1 hour of credit towards
your 10 hours this week.
• How? Place your cursor and left click your
mouse on the participant window. On your
keyboard, hold down the SHIFT and PRINT
SCREEN keys. Then open a Word document
and paste (Ctrl + V). Last, attach your word
document to an email and send it to your
instructor.
Final Comments
• This session has been recorded for you to play back
and view at any time.
• If you have any questions regarding this topic at a
later time, don’t hesitate to contact your instructor.
• Don’t forget to use the Smarthinking tutor feature
within your class site. A tutor is available to you 24
hours a day.
Thank you for coming!
I hope you will take advantage of
our future LIVE virtual lessons and
will attend some of those sessions
as well.
Have a great day!