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Algebra 1 Notes Questions/Main Ideas: Name: ________________________ Period: _______Date: ____________ TOPIC: STANDARD DEVIATION Recall: a statistic Describes a data set (tells something about a data set) Standard Deviation is a statistic that measures the spread of the data AWAY FROM THE MEAN (average). Think of Deviation as “how far from the average” The symbol for Standard Deviation is called “Sigma” The buttons to push to get L1 are: Where have we seen the before? In the same place we find X After you put a data set into the L1 then press STAT ENTER 1 Where do you find the sigma? The 5th item down in the list Use your calculator to find the Standard Deviation and the mean of the following data set. X ______ { 2, 4, 5, 5, 7, 7, 8, 10 } Standard Deviation is used to measure a The sample mean x̄ is what you compute from your random sample in order to ESTIMATE the population mean μ. The sample mean is summed over the sample size n. The population mean is summed over the population size N or even ∞, if you knew the whole population. Usually you do not, which is why you take a sample in the first place. By estimating μ with x̄ you have an error, called the sampling error. They are not the same thing. Many different samples will produce different x̄ 's for the same population. The Distance above and below the mean value of the data set. _____ Map the data set on this number line { 2, 4, 5, 5, 7, 7, 8, 10 } X or 0 -3 3 -2 “Mean” 6 -1 9 +1 +2 12 +3 the Count of the Standard Deviations usual Which values in the data set are within one standard deviation of the mean? Which values are between +1 and +2 ? Are any values beyond 2 away from the mean? ________ ________ ________ To do the following problem we need to know the mean and the standard deviation. X ___ 66.3 ___ Given the following data set { 53, 63, 62, 64, 66, 68, 70, 72, 79 } Determine: Which values are unusual ___ 6.84 __ _______ (How do we know “unusual” ? ) What is the value 2 standard deviations below the mean _______ Which value is within the first deviation from the mean _______ Which values are between -1 and -2 from the mean _______ How many values are below the mean? _______ Uses of Standard Deviation If the mean temperature over the past 100 years for the first day in June in the city of Eye Brow Kentucky is 89.5° Find the temperature that is 2 standard deviations below the mean if the Standard Deviation is 6.5° degrees. If the Height of the average full grown Collie is 37 inches with a Standard Deviation of 2.5 inches. Find the Height of a dog that is three standards above the mean. If the average weight of a bottle of Ketchup is 567 grams with a standard deviation of 5.5 grams, find the weight of a bottle that is 4 standard deviations below the mean. If the average bottle of ketchup weighs 567 grams. How many standards above a normal bottle is a bottle that weighs 600 grams. Use a standard Deviation of 5.5 g Standard Deviation Facts is for data that is normally distributed 68%, Normally distributed is Data the is not skewed Data that is centered close to the mean Data that generally follows the 68, 95, 99 rule 95%, 99%