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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.