Clip A
<<show clips below>>
A set of data with the numbers 2, 4, 6, 8, 10 that
has an arrow pointing to the number 6.
Today we are going to learn about some
applications of mean. The mean of a data set,
sometimes called average, can be used in various
different applications.
<<show clips below>>
Some examples of this are batting average in
A drawn image of a batter with his batting average baseball, calculating your grade in a course,
next to him.
bowling, as well as various statistical calculations.
A bowling looking at a sheet that shows 3 game
scores and his average for the night.
<<Show clips below>>
On screen show the following numbers on a
number line:
25, 30, 45, 60, 90
Draw an arrow pointing to where 50 is on the
number line.
Continue showing the numbers, but below add
the value 50
To make sure you are still familiar with how to
calculate mean, let’s look at a set of data. We can
find the mean of the set of data here by taking the
sum of the digits shown divided by the total
number of digits, which in this case equals 50.
Clip A Question
On Screen
12, 12, 24, 36, 50, 60, 88
Question Text
What is the mean of the above data set?
A) 12
B) 36
C) 47
D) 50
Clip B
<<Show clips below>>
A clip of a family packing clothes into suitcases.
Great job! Now let’s look at a real life application
of using mean to find the average temperature for
a week. The news will always give you an update
on weather. They like to give a forecast so that
people expect what the temperature will be.
This kind of data is useful if you are going on
vacation. You will know what kind of weather to
expect and what type of clothes to bring. This clip
shows 2 different values, the high temperature
and the low temperature. Even though this is
different than just a normal set of numbers, the
mean is calculated the same way.
Clip B Question
On Screen
<<An image like the one below but showing 7
thermometers with the numbers 66, 68, 64, 70,
76, 74, 72>>
Question Text
What is the mean temperature for next week with
the temperature shown above?
A) 67 degrees
B) 68 degrees
C) 69 degrees
D) 70 degrees
Clip C
<<Show clips below>>
Show the numbers 10, 20, 20, 30, 70 on a number
line.
Point to the number 20 and above the arrow
display “Median”
Point to the number 50 and above the arrow
display “Mean”
Let’s take a look again at some difference
between measures of center. The mean calculates
the average of the values whereas the median
calculates the middle number of a data set.
<<Show clips below>>
Aerial view of a city showing 2 areas, one with
extremely nice houses that has fewer houses than
another area with normal houses.
Draw an arrow to each area, labeled as expensive
and inexpensive
These are both measures of center, but their
applications can differ immensely. When looking
to buy a home in a town, you can look at average
home value to help you determine what area you
should look at. This image shows a small area of
expensive houses and a large area of inexpensive
houses.
Aerial view of a city showing 2 areas, one with
extremely nice houses that has fewer houses than
another area with normal houses – This time show
the expensive area with $$$ and the inexpensive
with $ on top of each area.
If we took the average of the homes, the value
might seem large, but if you took the mean of
each area separately, you would get a value more
appropriate to the home you were looking to buy.
Clip C Question
On Screen
Show 4 images of homes with the following prices
below each one.
$90,000
$95,000
$87,000
$80,000
Question Text
What is the mean value of the 4 homes shown
above?
A) $87,000
B) $87,500
C) $88,000
D) $90,000
Clip D
<<show clips below>>
12 35 44 ____ 56
Another way to use mean is the real world is when
you need to find a missing value. In cases where
you have a missing value and know the mean, you
can use trial and error or equations to help you
find the answer.
<<show clips below>>
Student looking at multiple tests with grades on 3
of them, then a 4th with a question mark on it
Being able to work backward like this can be
applied to different scenarios. If you need to get a
certain grade in a class, and you know what you
go for the first 3 quarters, you can then determine
what you need to get in quarter for so that your
average for the class is what you intended.
Clip D Question
On Screen
Show a batter on screen and to the right of him a
column with the following:
Year 1
.302
Year 2
.299
Year 3
.288
Year 4
.290
Year 5
?
Question Text
Being what is known as a “300” hitter in baseball is
a very hard feat to achieve. You can see 4 out of 5
years of a batters average on the screen. What
average does he need in year 5 to have a mean
batting average of .300?
A) .299
B) .300
C) .320
D) .321
Clip E
<<show clips below>>
Show a fraction with the following:
30 + 40 + 50 + 60 + 70
=?
5
Replace the “?” with the number 50
When trying to find the missing value in a problem
with mean you are working backward from where
you normally would. You are usually given the
value of each element, which also gives you the
total number of elements. So you are missing 1
thing, the mean.
<<show clips below>>
30 + 40 + ? + 60 + 70
= 50
5
Replace the “?” with the number 50
When you have a missing value you are still given
2 out of the 3 pieces of information necessary to
solve the problem. You know the number of
elements and the mean, so you just need to
determine the missing value with trial and error or
with an equation.
<<show clips below>>
1 + 3 + 5+ ? +10
=5
5
5 × 5 = 25
25 – 1 – 3 – 5 – 10 =
In this example on screen you know the number
of elements and the mean, so you need to find the
missing value. One way to do this is to multiply
your number of elements, 5, by the mean, which
is also 5 in this problem… giving you 25. Now
subtract the values you know to find the missing
element.
Clip E Question
On Screen
<<Display the following numbers across the
screen>>
8 15 ___ 16 18 22
Question Text
What is the missing element in the problem on
screen to have a mean value of 16?
A) 15
B) 17
C) 19
D) 20
Clip F
<<Show clips below>>
Mean
Median
Mode
Range
Being able to differentiate between the different
types of statistical measurements is extremely
important so that you can effectively apply that
information. Each of these values has an
important use, but they must be used properly.
<<Show clips below>>
Show a data set that has an outlier to the far right.
Draw an arrow to the outlier.
Knowing how to apply the difference between
mean and median is useful for different measures
of center. Median is useful when there are outliers
in your data, but in most other cases the mean
would be most beneficial.
<<Show clips below>>
Show a set of houses on a street with values
between 800 and 1,000 kWh on each.
Mean can be used in a variety of ways, such as
determining your average grade in a course or
determining how much electricity most
households in an area use each month.
Clip F Question
On Screen
A) The middle number in a set of data.
B) The number that is repeated the most in a
set of data.
C) The total number of elements in a data set
divided by the total of the elements.
D) The sum of that data divided by the
number of elements in the set.
Question Text
What is the definition of mean?
<<On screen show A B C D>>
D being correct.
Clip G
<<Show clips on screen>>
Show an image like the one below, but just 3
games for 1 person.
Another application of mean is in bowling. In
bowling you have 10 rounds in each game, and
you usually play 3 games each night. The most
points you can get in a game is 300. You can use
mean to determine their average score for the
night.
<<Show clips below>>
Show another bowling score image with the
following 3 game scores:
255
270
295
Look at the game scores for Peter on his score
sheet. He got a 255, 270, and 295. What would his
mean score be for the night? What would he have
bowled in game 1 to have a mean score of 280 for
the night?
<<show clips on screen>>
255 + 270 + 295
3
Fade out the 255 and replace with equation
below:
? + 270 + 295
= 280
3
His mean for the first 3 games can be found by
taking the sum of the games divided by the
number of games played, just like finding mean
for any data set. To find out how he could have
got a 280 for the night, you need to work
backward to find the missing element.
Clip G Question
On Screen
Game 1 – 175
Game 2 – 200
Game 3 – 180
Game 4 – 185
Game 5 – 199
Game 6 – 225
Game 7 – 280
Game 8 –290
Game 9 - 300
Question Text
John bowled 9 games tonight. What was his mean
score for the first 6 games?
A) 190
B) 194
C) 220
D) 226