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The mean does not always show us enough information about a set of data. The “spread” of a set of data is often also useful to calculate.A deviation is the difference between an individual value in a set of data and the mean for the data.For a population: deviation =For a sample, deviation =The variance and the closely-related standard deviation are measures of how spread out a distribution is. In other words, they are measures of variability.Variance: the mean of the squares of the deviations.Population Variance:Sample Variance:Standard Deviation: the square root of the mean of the squares of the deviations.Population Standard Deviation?:Sample Standard Deviation:*Note: The formula for a sample has n-1 in the denominator to compensate for the fact that a sample tends to underestimate the deviation in the population.If you are working with grouped data, you can estimate the standard deviation using the following formula:Population:Sample:Example 1 Calculate the mean, standard deviation and variance of the heights of everyone in the class.NameHeight (cm), x Deviation, x - μx-μ2FarahAminahLaurenChrisSaadVictorRachelTylerGemmaNikkiCodieDanielAndrewSarahCarlyDarrenFeliciaDonnaAllyLinaAmmadKareemDavidNeeshaMashaHarjotRanaMs. KuehSum:Homework: pg. 148 #1, 6, 9ab ................
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