1. mean median once. I made sure to keep my mode out of that
CCCS Aligned
Mean,
I met a
mean median once. I made sure to keep my mode out of that
range!
Median,
Mode,
And Range
©Mike’s Math Mall

2. Are we
talking about my
my sister?
Part 1
Mean
The meaning of

3. Mean Mean – the average of a set of numbers.
Let’s talk about the meaning of mean!
Mean – the average of a set of numbers.
To find the mean of a data set, add up all the numbers, then divide by how many numbers make up that set.
I guess it’s because the words have the same meaning! Get it, Sparky? LOL!
If the mean
is really just the
average, why don’t
we use the word “average?”
This is
the very reason math gives me hives!

4. Let’s see how this works!
Mean
Let’s see how this works!
Several students were surveyed about the number of pets they’ve ever owned.
Here are the results: 5, 1, 8, and 6.
What is the mean number of pets?
Step 1: Find the sum of the numbers.
𝟓+𝟏+𝟖+𝟔= 𝟐𝟎
𝟐𝟎 𝟒 =
Step 2: Divide the sum by the count. 𝟓
Mean = 5 pets

5. Mean You try it! 1. {𝟖, 𝟏𝟏,𝟓} Mean = 𝟖 2. {𝟕, 𝟏𝟑, 𝟗, 𝟔,𝟏𝟎} Mean = 𝟗
Find the mean for each set of numbers.
1. {𝟖, 𝟏𝟏,𝟓}
Mean = 𝟖
2. {𝟕, 𝟏𝟑, 𝟗, 𝟔,𝟏𝟎}
Mean = 𝟗
3. {𝟏𝟐, 𝟐𝟑, 𝟏𝟔, 𝟒, 𝟏𝟏,𝟔}
Mean = 𝟏𝟐
4. {𝟏𝟎, 𝟓, 𝟖,𝟑}
Mean = 𝟔.𝟓 5.
A group of girls listed how many rings
each had: 𝟑, 𝟕, 𝟒, 𝟏𝟐, 𝟓, 𝟗, 𝟓, 𝟑, and 𝟔.
Find the mean number of rings!
𝟔 rings

6. to the middle of triple, fudge-filled jelly donuts!
I love getting
to the middle of triple, fudge-filled jelly donuts!
Part 2
Median
Getting into the Middle of

7. Median – the middle number. To find the median, list a set of numbers
Middling with Medians!
Median – the middle number.
To find the median, list a set of numbers
in order (from least to greatest), and then find the number in the middle.
Why don’t
we just call the median “the middle number?”
Because it’s kinda fun seeing that crazy Sparky face!
Must…
find…happy
place…now!

8. Median Example 1 Step 1: List all the numbers in order. 𝟕𝟐, 𝟕𝟔, 𝟖𝟓,
Here are several math quiz scores: 𝟗𝟏, 𝟖𝟖, 𝟕𝟐, 𝟏𝟎𝟎, 𝟗𝟔, 𝟖𝟓, 𝟏𝟎𝟎, 𝟗𝟑, and 𝟕𝟔.
What is the median score?
Step 1: List all the numbers in order.
(It helps to cross them off as you go) 1 2 3 4 4 3 2 1
𝟕𝟐,
𝟕𝟔,
𝟖𝟓,
𝟖𝟖,
𝟗𝟏,
𝟗𝟑,
𝟗𝟔,
𝟏𝟎𝟎,
𝟏𝟎𝟎
Step 2: Count to find the middle number.
is the median 𝟗𝟏

9. What is the median point total?
Example 2
Ben’s point totals in basketball games: 𝟏𝟕, 𝟐𝟎, 𝟖, 𝟏𝟏, 𝟏𝟑, 𝟑, 𝟖, and 𝟏𝟔.
What is the median point total?
1. List the numbers in order.
2. Count. 1 2 3 3 2 1
3, 8, 8, 11, 13, 16, 17, 20
3. After counting, we have two middle numbers.
4. Add them and divide by 2.
𝟏𝟏+𝟏𝟑=𝟐𝟒
𝟐𝟒÷𝟐=𝟏𝟐
The median is 𝟏𝟐

10. Median Think about it! When trying to find the median:
If there is an odd number of data numbers, there will always be 1 middle number.
If there is an even number of data numbers, there will always be 2 middle numbers.
The two
middle number
thingy is a little
annoying!
Only my
momma calls
me by my full name!
You can handle it, Sparkington! You’re a trooper!
I stand corrected, Sir Sparkles!

11. Median Give it a try! 1. {𝟓𝟑,𝟓𝟖,𝟓𝟔,𝟓𝟒, 𝟓𝟏} 2. {𝟗,𝟑,𝟒,𝟏𝟐, 𝟔, 𝟏𝟎}
Find the median for each set of numbers.
1. {𝟓𝟑,𝟓𝟖,𝟓𝟔,𝟓𝟒, 𝟓𝟏}
2. {𝟗,𝟑,𝟒,𝟏𝟐, 𝟔, 𝟏𝟎}
The median is 𝟓𝟒
The median is 𝟕.𝟓
3. {𝟏𝟒,𝟕, 𝟏, 𝟑, 𝟖, 𝟕, 𝟐, 𝟏𝟐, 𝟔}
The median is 𝟕
4. {𝟏𝟏,𝟖, 𝟏𝟗, 𝟗, 𝟓, 𝟏𝟓, 𝟗, 𝟏𝟔, 𝟏𝟒, 𝟕, 𝟏𝟒, 𝟐𝟎}
The median is 𝟏𝟐.𝟓
5. Here are the results after a recent science quiz:
𝟗𝟓,𝟖𝟖, 𝟕𝟑, 𝟗𝟎, 𝟗𝟓, 𝟖𝟓, 𝟖𝟎, 𝟕𝟔, 𝟏𝟎𝟎, 𝟕𝟖, 𝟗𝟕
Find the median score.
The median is 𝟖𝟖%

12. the most of a three-alarm chili burrito!
Mode
Making the Most of
I just made
the most of a three-alarm chili burrito!
Part 3

13. List all the numbers in order. (It makes it easier to spot the mode)
Mostly mode!
Mode – a number that appears the most in a data set.
What is the mode of this data set? {𝟏𝟒,𝟏𝟐,𝟗,𝟕, 𝟒, 𝟏𝟎, 𝟏𝟔, 𝟖, 𝟔, 𝟏𝟒,𝟗, 𝟓, 𝟗}
List all the numbers in order.
(It makes it easier to spot the mode)
𝟒,𝟓,𝟔, 𝟕,𝟖,𝟗,𝟗,𝟗,𝟏𝟎,𝟏𝟐,𝟏𝟒,𝟏𝟒,𝟏𝟔
The mode is 𝟗

14. It is possible to have two or more modes.
Keep this in mind!
If no number occurs more than once in a set of numbers, there is no mode.
1, 3, 8, 9, 12, 13, 16, 19, 20, 22, 31
No mode
It is possible to have two or more modes.
2, 5, 5, 7, 10, 11, 15, 18, 18, 24, 25
The modes are 5 and 18

15. Find the mode for each data set.
Your turn!
Find the mode for each data set.
1. {𝟑,𝟖,𝟓,𝟒, 𝟓, 𝟕, 𝟔, 𝟏𝟏}
2. {𝟗,𝟏𝟑,𝟐,𝟏𝟎, 𝟔, 𝟖, 𝟏}
The mode is 𝟓
No mode
3. {𝟑𝟒,𝟑𝟕, 𝟑𝟏, 𝟒𝟑, 𝟒𝟖, 𝟑𝟕, 𝟒𝟐, 𝟑𝟐, 𝟑𝟏, 𝟑𝟕}
The mode is 𝟑𝟕
4. {𝟏𝟔,𝟐𝟏, 𝟗, 𝟏𝟗, 𝟏𝟓, 𝟏𝟔, 𝟏𝟎, 𝟏𝟏, 𝟏𝟒, 𝟕, 𝟏𝟖, 𝟗}
The modes are 𝟗 and 𝟏𝟔
5. Here are the results after a recent math quiz.
𝟏𝟎𝟎,𝟗𝟒,𝟖𝟖, 𝟖𝟑, 𝟗𝟎, 𝟕𝟓, 𝟖𝟑, 𝟖𝟎, 𝟗𝟒, 𝟕𝟓, 𝟕𝟖, 𝟖𝟓
Find the mode.
The modes are 𝟕𝟓, 𝟖𝟑, and 𝟗𝟒

16. the monkeys and elephants play!
…where
the monkeys and elephants play!
Range
Home, Home
on the
Part 4

17. Excellent observation!
Range
Keep it in Range!
Range – the difference between the lowest and highest values in a data set.
Example: {𝟗,𝟏𝟎,𝟕, 𝟏𝟒}
Here, the lowest value is 7.
𝟏𝟒−𝟕=𝟕
The highest value is 14.
Easy
peasy lemon squeezy!
The range is 𝟕
Excellent observation!

18. Range Try this example! The range is 𝟏𝟖 List all the numbers in order.
What is the range of this data set? {𝟐𝟒,𝟏𝟕,𝟖,𝟔, 𝟏𝟒, 𝟗, 𝟏𝟓, 𝟐𝟏, 𝟏𝟔, 𝟏𝟎}
List all the numbers in order.
(This helps find the highest and lowest values)
𝟔,𝟖,𝟗,𝟏𝟎,𝟏𝟒,𝟏𝟓,𝟏𝟔,𝟏𝟕,𝟐𝟏,𝟐𝟒
𝟐𝟒−𝟔=𝟏𝟖
The range is 𝟏𝟖

19. If you said that it would bring the mean down, you’re correct!
FYI
Discovering Outliers!
Outlier – a value that “lies outside” (is much smaller or larger than) most of the other values in a data set.
What is the outlier of this data set? {𝟖𝟎, 𝟖𝟐, 𝟏𝟎𝟎, 𝟐𝟒, 𝟗𝟒, 𝟕𝟖, 𝟖𝟕, 𝟗𝟖}
24 is the outlier.
Question: How would this outlier effect the mean of this data set?
If you said that it would bring the mean down, you’re correct!

20. Mean Median Range Mode Let’s see if you can put it all together!
Use the data set below to answer the following questions.
Here are Duffy Divot’s golf scores for the year. Find the mean, median, mode, and range of his scores.
{𝟖𝟑, 𝟖𝟎, 𝟏𝟎𝟔,𝟖𝟓, 𝟖𝟑,𝟖𝟔, 𝟖𝟐, 𝟕𝟗}
Mean = 𝟖𝟓.𝟓
Median = 𝟖𝟑
Mode = 𝟖𝟑
Range = 𝟐𝟕
Is there an outlier? If so, what does it do to the mean score?
Range
Mode
Yes. The outlier, 106, raises the mean score.

21. weird that I actually kinda understand this stuff, Sir?
Mean
Median
To be honest, Sparky, that’s not what I’m finding a little weird right now.
Is it a little
weird that I actually kinda understand this stuff, Sir?
It’s my
breath isn’t
it?
Rock on!
Well, I guess I’ll comb ya…err,
I mean…catch ya later!
Nope! It’s not your breath!
Range
Mode