Download The width of a rectangle is seven less than twice the length. If the

The width of a rectangle is seven less than twice the length. If the perimeter of this
rectangle is 100 inches, find the area.
The equation below shows how much it costs to produce n iPads. How many iPads can
be produced for $950?
2
C = −4 x + 5 x + 1200
Mrs. Lammert bought Riley some new toys and treats. She bought her 5 toys and 10
treats for $47.50. Mr. Lammert didn’t realize this and went out and bought her 3 toys
and 8 treats for $31. How much is one toy?
9.4 Distributions
Normal Distribution There are many cases where the data tends to be
symmetrical around a central value with no bias left or right, and it gets close to
a "Normal Distribution" like this:
Distributions
We say the data is "normally distributed" or “symmetric”:
The Normal Distribution has:
• Mean = Median = Mode
• Symmetry about the center
• 50% of values less than the mean
and 50% greater than the mean
Distributions
Data can be "distributed" in different ways when it is not symmetrical.
Skewed Left
(tail is longer on left)
Skewed Right
(tail is longer on
right)
Bimodal
It can have more than 2
modes
http://www.mathsisfun.com/data/standard-normal-distribution.html
Distributions
Determine the distribution of each graph.
Distributions
Determine the distribution of each graph.
Distributions
Standard Deviation: is a statistic that tells you how tightly all the various
examples are clustered around the mean in a set of data.
• A low standard deviation means that the data is very closely related to the
average, thus very reliable.
• A high standard deviation means that there is a large variance between the
data and the statistical average, thus not as reliable
Distributions
Even though both classes have the
Same mean, class A displays scores
that are more closely clustered to
the mean. It has a smaller
standard deviation.
Distributions
Some examples of situations in which standard deviation might help to
understand the value of the data:
Explain what each situation suggests.
• A class of students took a math test. Their teacher found that the mean score
on the test was an 85%. She then calculated the standard deviation of the
other test scores and found a very small standard deviation which
suggested:
• A dog walker wants to determine if the dogs on his route are close in weight
or not close in weight. He takes the average of the weight of all ten dogs. He
then calculates the variance, and then the standard deviation. His standard
deviation is extremely high. This suggests
Distributions
Explain what each situation suggests.
• A market researcher is analyzing the results of a recent customer survey. He
wants to have some measure of the reliability of the answers received in the
survey in order to predict how a larger group of people might answer the
same questions. A low standard deviation would show:
• A weather reporter is analyzing the high temperature forecasted for a series
of dates versus the actual high temperature recorded on each date. A low
standard deviation would show:
http://examples.yourdictionary.com/examples-of-standard-deviation.html
Distributions
The mean for each both of these sets of data is the same. Which one has a
smaller standard deviation?
1) a.) 10, 100, 55, 50, 60, 75 35
2)
a.) 80, 75, 85, 79, 81, 82, 78
or
or
b.) 50, 60, 51, 61, 55, 54, 56
b.) 60, 100, 90, 70, 95, 65
Distributions
3) If we found the standard deviation of all of the student ages in this class
right now, would it be a large or small number?
If you all gathered together again in my classroom for your ten year
reunion, how would the standard deviation change?
4) If 5 is added to each observation in the following data set, what happens
to the standard deviation?
11, 15, 19, 25, 37, 42
Distributions
The area of a rectangle is 224 yards squared. If the length is two yards less than the
width, find the dimensions of the rectangle.