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Welcome to IRSCs LIVE Virtual Lesson on

- Mean, Median, Mode, and Range
- Instructor Mrs. DiMartino

How to participate in this session

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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?

- 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
- Add the numbers
- 6 11 7 24
- 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
- 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
- Place the numbers you are given in value order.

3, 4, 6, 7, 9 - 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
- Place the numbers you are given in value order.

2, 6, 7, 8, 9, 12 - Find the middle number.
- 2, 6, 7, 8, 9,

12 - Wait a minute! There isnt a middle

number!!!

Median (Ex2 continued)

- When there are two numbers in the middle
- Locate the two middle numbers. (7 and 8)
- Add them together. 8 7 15
- Divide that number by 2. 15 / 2 7 ½
- The median is 7 ½

Example 3 Finding the Median

- Find the median of
- 4, 9, 5, 13, 7
- Place the numbers you are given in value order.

4, 5, 7, 9, 13 - 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?

- First, put the numbers in order.
- Then count how many there are of each number.
- 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
- First, put the numbers in order.
- 2, 3, 3, 6, 7, 7, 7,

8, 9 - 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
- First, put the numbers in order.
- 2, 3, 3, 3, 4, 4, 6, 6,

6, 8 - 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
- First, put the numbers in order.
- 3, 4, 6, 8, 9, 9, 11,

12, 12, 12 - 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?

- First, put the numbers in order.
- Locate the largest number and the smallest

number. - 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
- 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

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Example 2 Finding the range

- Find the range of this set of numbers
- 22, 16, 17, 8, 12
- 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

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Example 3 Finding the Range

- Find the range of this set of numbers
- 1, 3, 9, 4, 20, 6
- 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 - 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, Sarahs test

scores in math were 94, 88, 89, 78, and

100. What is her test average (mean)? - Solution
- Order the data from least to greatest.
- 78, 88, 89, 94, and

100 - Add the numbers.
- 78 88 89 94 100

449 - 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
- 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, dont hesitate to contact your

instructor. - Dont 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!