Standard deviation = sqrt(variance)
Variance = E[X2] - E[X]2
E[X] = sum(X)/n = 35/9, so E[X]2 = 1225/81
E[X2] = sum(X2)/n = 189/9 = 1701/81
Variance = 476/81
Standard deviation = sqrt(476/81) ~ 2.42
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To Find Average Deviation 1. Find the average value of your measurements. 2. Find the difference between your first value and the average value. This is called the deviation. 3. Take the absolute value of this deviation. 4. Repeat steps 2 and 3 for your other values. 5. Find the average of the deviations. This is the average deviation The average deviation is an estimate of how far off the actual values are from the average value, assuming that your measuring device is accurate. You can use this as the estimated error. Sometimes it is given as a number (numerical form) or as a percentage. To Find Percent Error 1. Divide the average deviation by the average value. 2. Multiply this value by 100. 3. Add the % symbol.
3.5* * * * *The mean deviation of ANY set of numbers must always be zero.
Variability is determined by the how numbers are distributed across the set of numbers. There are several ways of measuring this the most common is standard deviation. To find standard deviation you first find the average of the set by adding them all up and dividing by the amount of numbers in the set. Then you find the square of each number in the set minus the average. You add all these values up, multiply them by 1/the number of items in the set, and take the square root. As an example the set {2,5,3,6} has much less variability as measured by the standard deviation than {2000,-1000,-500,484} even though they both have the same average. The firsts average is (2+5+3+6)/4 or 4. The standard deviation is the square root of(((2-4)^2+(5-4)^2+(3-4)^2+(6-4)^2)*1/4) or about 1.58113883. The standard deviation of the second set that has the same average as the first is the square root of (((2000-4)^2+(-1000-4)^2+(-500-4)^2+(484-4)^2)*1/4) or 1170.09059.
What you are trying to find is the average or mean. You find this by adding all the numbers in a set together and divide by the amount of numbers you added. Example: 1, 1, 2, 2, 3, 3. Find the average (mean). Add all the numbers in the set together: 1 + 1 + 2 + 2 + 3 + 3 = 12 Divide by the amount of numbers you added: You added together 6 numbers: 12 ÷ 6 = 2. Mean of {1, 1, 2, 2, 3, 3} = 2.