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>>
Add the title batting average to the image below
Some examples of this are
batting average in baseball,
calculating your grade in a
course, bowling, as well as
various statistical calculations.
Image 1
http://www.theperfectaffirmation.com/blog/wpcontent/uploads/2014/07/hitter.jpg
http://1.bp.blogspot.com/_54Iv-ydMd5M/TOGLQlb_BI/AAAAAAAAAAw/AEzk_A7h5oA/s1600/Bowlscrsht10.JPG
Image 2
<<Show clips below>>
<<Number line example to use can be found at the link below, leave
tick marks blank>>
http://exchangedownloads.smarttech.com/public/content/ff/ff8ef5d7e0a1-4e8f-955f-24aa885a2357/previews/medium/0001.png
Image 3
On screen show the following numbers on a number line:
25, 30, 45, 60, 90 (these should be the only numbers currently on the
number line)
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 B
<<Show clips below>>
http://www.hairfinder.com/fashion/packing.jpg
Image 4
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.
http://sanibelsusan.files.wordpress.com/2014/01/7- This kind of data is useful if you are going on
day-forecast-01-10-14.jpg Image 5
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 C
<<Show clips below>>
<<Number line example to use can be found at the link below,
leave tick marks blank>>
http://exchangedownloads.smarttech.com/public/content/ff/ff8
ef5d7-e0a1-4e8f-955f24aa885a2357/previews/medium/0001.png
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.
Image 6
Show the numbers 10, 20, 20, 30, 70 on a number line. (these
should be the only numbers show on the number line, use the
first tick mark as 10 counting by 10’s)
Point to the number 20 and above the arrow display “Median”
Point to the number 50 and above the arrow display “Mean”
<<Show clips below>>
http://upload.wikimedia.org/wikipedia/commons/c/cb/Aerial_vi
ew_of_city_of_Oakland_1.jpg
Image7
Draw an arrow to the area below the highway on screen and
draw another arrow to the area above the lake in the middle of
the image
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.
Where the arrow is pointing below the highway, add $$$$
Where the other arrow is pointing, add $
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 D
<<show clips below, drawn on screen>>
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>>image 8
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.
On the bottom of this image add “70 + 80 + ? + 85 = 80
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 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 the numbers 10, 12, 13, 15, 17, 40 on screen
Draw an arrow to 40.
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>> Image 9
http://www.tubewalker.com/images/central/liverpool_street_t
o_leytonstone/full_size/liverpool_street_to_leytonstone221.jp
g
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.
Above each house show a value between 800 and 1,000 kWh
on each.(the numbers don’t matter)
Clip G
<<Show clips on screen>>
http://www.someblogsite.com/images/bowlingspeed-17.jpg
Image 10
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 on screen the following numbers:
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.