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Difference between Simple Standard Deviation, Population Standard Deviation, Short- term & Long- Term Standard DeviationSample Standard Deviation: A?sample standard deviation?is an estimate, based on a sample, of a population?standard deviation. Example:Let's say we wanted to calculate the standard deviation for the amounts of gold coins pirates on a pirate ship have.There are 100 pirates on the ship. In statistical terms this means we have a population of 100. If we know the amount of gold coins each of the 100 pirates have, we use the?standard deviation equation for an entire population:What if we don't know the amount of gold coins each of the 100 pirates have? For example, we only had enough time to ask 5 pirates how many gold coins they have. In statistical terms this means we have a sample size of 5 and in this case we use the?standard deviation equation for a sample of a population:The rest of this example will be done in the case where we have a sample size of 5 pirates, therefore we will be using the standard deviation equation for a sample of a population.Here are the amounts of gold coins the 5 pirates have:4, 2, 5, 8, 6.Now, let's calculate the standard deviation:1. Calculate the mean:2. Calculate??for each value in the sample:3. Calculate?:4. Calculate the standard deviation:The standard deviation for the amounts of gold coins the pirates have is 2.24 gold coins.Population standard deviation: Example:You grow 20 crystals from a solution and measure the length of each crystal in millimeters. Here is your data:9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4Calculate the population standard deviation of the length of the crystals.Calculate the mean of the data. Add up all the numbers and divide by the total number of data points.(9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4) / 20 = 140/20 = 7Subtract the mean from each data point (or the other way around, if you prefer... you will be squaring this number, so it does not matter if it is positive or negative).(9 - 7)2?= (2)2?= 4(2 - 7)2?= (-5)2?= 25(5 - 7)2?= (-2)2?= 4(4 - 7)2?= (-3)2?= 9(12 - 7)2?= (5)2?= 25(7 - 7)2?= (0)2?= 0(8 - 7)2?= (1)2?= 1(11 - 7)2?= (4)22?= 16(9 - 7)2?= (2)2?= 4(3 - 7)2?= (-4)22?= 16(7 - 7)2?= (0)2?= 0(4 - 7)2?= (-3)2?= 9(12 - 7)2?= (5)2?= 25(5 - 7)2?= (-2)2?= 4(4 - 7)2?= (-3)2?= 9(10 - 7)2?= (3)2?= 9(9 - 7)2?= (2)2?= 4(6 - 7)2?= (-1)2?= 1(9 - 7)2?= (2)2?= 4(4 - 7)2?= (-3)22?= 9Calculate the mean of the squared differences.(4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9) / 20 = 178/20 = 8.9This value is the variance. The variance is 8.9The population standard deviation is the square root of the variance. Use a calculator to obtain this number.(8.9)1/2?= 2.983The population standard deviation is 2.983Short term Standard Deviation:The Short-term standard deviation estimates standard deviation within, and is a measure of how widely values are dispersed from the average value (the mean) due only to the effect of white noise.It is used to calculate Short-term Process Capability (i.e.: Cp and Cpk).Long term standard deviation:The standard deviation long-term estimates total standard deviation of the process, and is a measure of how widely values are dispersed from the overall average value (the grand mean) due to white noise and black noise.Used to calculate process long-term capability (i.e.: Pp and Ppk) and PPM defective. ................
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