Statistics Notes ai
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- Standard Deviation A statistic that tells us
- Step 4
- Normal Distribution
Statistics Notes AII. 11 Heights:
Paul Sturgess walks in the room. He is the tallest member of the Harlem Globetrotters at 7ft. 8 inches. How is his height going to influence the mean, median, and mode?
If one of Mrs. Luckett’s 34 inch tall nieces comes in this class, how will her height influence the measures?
Mean, Median, and Mode are central tendencies. Unlike these, the Standard Deviation of the data is used to describe the span of the data. Let’s look at your height data.
Standard Deviation A statistic that tells us: How far from ___________________ a certain piece of data is. How _____________ _________________ the data items are in our data set. The mathematic symbol for standard deviation is the lower case Greek letter _____________ and it looks like this: Calculating Standard Deviation Data Set = {600, 470, 170, 430, 300} Step 1: Calculate the ____________ . m = _____________ mm. Step 2: Calculate the _________________ from the mean for each element (xi) in the data set. Step 3: ______________ each difference from Step 2. Step 2 Step 3 600 - m = ______________ ______________ 470 - m = ______________ ______________ 170 - m = ______________ ______________ 430 - m = ______________ ______________ 300 - m = ______________ ______________ Step 4: Find the mean m (average) of the numbers in Step 3. We call this number the ________________ and is represented by the math symbol σ2 Step 5: The standard deviation is the ________________ ______________ of the variance. s = _________________ Normal Distribution- Has data that vary randomly from the mean. The graph of a normal distribution is called the Normal Curve. The mean, median, and mode are equal The normal curve is bell shaped and symmetric about the mean The total area under the curve is equal to one The normal curve approaches but never touches the x-axis as it extends from the mean Contains inflection points at µ - σ and µ + σ, where the curve changes from curving upward to downward. (µ is the mean)(σ is the standard deviation) 
The mean gives the location of the line of symmetry and the standard deviation describes how much the data are spread out. 
A standard normal distribution has a mean of 0 and a standard deviation of 1. It also has an area under the curve of 1. 
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