CALCULATING STANDARD DEVIATION WORKSHEET



Name: Date:Stats 1Stats.17.Standard Deviation - NotesNormal Distribution1428751270039814501238250057150149860Standard DeviationThe standard deviation for a set of data describes how spread out the numbers are!center381000center12065The two distributions shown above have the exact same ____________, but they have very different _________________ ________________.The smaller the standard deviation, the ____________ the scores are on average to the mean. The larger the standard deviation, the _____________ the scores are on average to the mean. The standard deviation is the average __________________ from the ____________.σ= i=1nxi-x2n-1Follow the steps below to calculate the standard deviation!Step 1: Arrange the scores in the Score column of the table in order from the smallest to the largest.Step 2: Find the mean of the data setStep 3: Subtract each of the scores from the mean. Record the difference in the Difference from the Mean column of the table. Be sure to record whether the answer is positive or negative. (i.e.:4-5=-1,7-5=-2)Step 4: Find the square of each number in the Difference from the Mean column and record the result in the Square of the Difference column (i.e.:Step 5: Record the number of items in the data set, n. Step 6: Find and record the Sum of the (Difference from the Mean)Step 7: Divide the Sum of the (Difference from the Mean) by the degrees of freedom, n – 1. This quotient is called the Variance of the data. Step 8: Find the standard deviation by finding the square root of the Variance.Practice Problem #1:The junior high basketball team played 20 games. Find the standard deviation for the number of baskets scored in fourth quarter of each game for a sample of ten games: 8, 4, 6, 6, 7, 7, 9, 4, 8, 5.ixixi-x(xi-x)i=1nxi=i=1n(xi-x)2 =Sample size: n = Mean: x = i=1nxin = Degrees of Freedom: n-1= variance :σ2= i=1nx1-x2(n-1)= Standard deviation = square root of variance Standard deviation: σ= Practice Problem #2A sample of student test scores from the 10th grade English classes was collected. Find the standard deviation for the following test scores. Use the chart below to record the steps.85, 100, 92, 96, 87, 94, 75ixixi-x(xi-x)i=1nxi=i=1n(xi-x)2 =Sample size: n = Mean: x = i=1nxin = Degrees of Freedom: n-1= variance :σ2= i=1nx1-x2(n-1)= Standard deviation = square root of variance Standard deviation: σ= Practice Problem #3Find the standard deviation for the following test scores collected from Science classes at all grade levels. Use the chart below to record the steps.22, 99, 102, 33, 57, 75, 100, 81, 62, 29ixixi-x(xi-x) ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download