Download File

Warm Up 11/16/15
Radical Product Property
You can rewrite a radical as the product of two radical factors of its radicand !
a b
ab
ONLY when a≥0 and b≥0
For Example:
9  16  9 16  144  12
9  16  3  4  12
Equal
Radical Quotient Property
You can rewrite a radical as the quotient of the radical numerator of the radicand divided by the radical
denominator of the radicand.
a

b
a
b
ONLY when a≥0 and b>0
For Example:
64
16
64
16

64
16

 4 2
8
4
2
Equal
Rationalizing a Denominator
The denominator of a fraction cannot contain a radical. To
rationalize the denominator (rewriting a fraction so the
bottom is a rational number) multiply by the same radical.
Simplify the following expressions:
5 2
5 2
5
2



2
2
2 2
2
 
6 3 6 3 3 2 3 2 3
6 3
3






2
35
5
15
53
3 5 3
5 3
6
 
Warm Up 11/17/15
You can use the internet to help you
find the answer!
Interpret the stem and leaf
Plot to the right to answer
The question:
The librarian at the public
Library counted the number
Of books on each shelf.
How many shelves have at least
45 books but fewer than 65
Books?
Books per shelf
Stem
Leaf
1
1127
2
48
3
46
4
45699
5
389
6
233
7
34456
Mean, Median, Mode and
Range
The Basics of Statistics
Did You Know…
That you
probably use
Statistics such
as Mean,
Median, Mode
and Range
almost every day
without even
realizing it?!?
This week We Will Learn…
• Mean
• Median
• Mode
• Range
• And how to use these in everyday
life, as well as the classroom!
What Do We Already Know?
Sure, the words “Mean, Median, Mode
and Range” all sound confusing…
But what about the words we already
know, like Average, Middle, Most
Frequent, and Difference?
They are all the same ideas!
Mean
• The mean is the Average of a
group of numbers
• It is helpful to know the mean
because then you can see which
numbers are above and below
(in terms of value) the mean
• It is very easy to find!
Mean Example
Here is an example test scores for Ms.
Math’s class.
82 93 86 97 82
To find the Mean, first you must add up all of the
numbers.
82+93+86+97+82=440
Now, since there are 5 test scores, we will next
divide the sum by 5.
440÷5=
88
The Mean is 88!
Now YOU try it!!!
This is the Stat Family!
Dad
34
Mom
Katie
33
Jack
Alex
5
5
1
Mean
Here are the ages again…
Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
What is the Mean?
Remember… Mean is the AVERAGE
Try it on your paper and see what you come up
with!
Mean
Remember, to find the mean, we have to first add
up all of the numbers.
34+33+5+5+1= 78
Then, since there are 5 people in the family, we
next divide by 5.
78÷5= 15.6
The Mean in this case is 15.6
Warm Up 11/18/15
• What is the mean of the following data set?
• {105, 223, 458, 1,016, 557)
Median
• The Median is the middle value
of a set of numbers.
• The first step is always to put
the numbers in order.
Median Example
•
First, let’s examine these five test scores.
78 93 86 97 79
We need to put them in order.
78 79 86 93 97
The number in the middle is 86
78 79 86 93 97
In this case, the Median is 86!
Median
Example
#2
Now, let’s try it with an even number of test scores.
92
86
94
83
72
88
First, we will put them in order
72 83 86 88
92
94
This time, there are two numbers in the middle, 86 and 88
72 83 86 88
92
94
Now we will need to find the Average/Mean of these two
numbers, by adding them and dividing by two.
86+88= 174
174÷2= 87
Here the Median is 87
Median
Here are the ages again…
Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
What is the Median?
Remember… Median is the MIDDLE NUMBER
Try it on your paper and see what you come up
with!
Median
Remember, to find the mean, we have to first put
all of the numbers in order.
34
33
5
5
1
The Mean in this case is 5
Warm Up 11/19/15
• What is the median of the following set of points
scored in a game by Brian?
• {12, 5, 31, 17, 14}
Mode
• The Mode refers to the number that occurs
the most frequently of a set of numbers.
• It’s easy to remember… the first two
numbers are the same! MOde and MOst
Frequently!
Mode Example
• Here is an list of temperatures for one week.
Mon. Tues. Wed. Thurs. Fri. Sat.
77°
79°
83°
77°
83°
82°
Sun.
77°
Again, We will put them in order.
77° 77° 77° 79° 82° 83° 83°
77° is the most frequent number, so the mode= 77°
Mode
Here are the ages again…
Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
What is the Mode?
Remember… Mode is the MOST FREQUENT
Try it on your paper and see what you come up
with!
Mode
Remember, to find the mode, we have to first
put all of the numbers in order.
34
33
5
5
1
The Mode in this case is 5
Warm up 11/20/15
• What is the mode of the following set of test scores
achieved by Steve?
• {98, 97, 85, 84, 98, 97, 97}
Range
• The range is the difference between the
highest and the lowest numbers of a set of
numbers.
• All we have to do is put the numbers in order
and subtract!
Range Example
• Let’s look at the temperatures again.
77° 77° 77° 79° 82° 83° 83°
The highest number is 83, and the lowest is
77.
All you need to do is subtract!
83-77= 6
In this case, the Range is 6
Range
Here are the ages again…
Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
What is the Range?
Remember… Range is the DIFFERENCE
Try it on your paper and see what you come up
with!
Range
Remember, to find the range, we have to first
put all of the numbers in order.
34
33
5
5
1
The highest age is 34, and the lowest is 1
Now we need to subtract to find the difference
34-1= 33
The range is 33