Standard Deviation – Practice Problems

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One of the statistical tools that can measure the “spread”, or variation, of a set of data is the standard deviation. It is represented by the symbol “σ” (small Greek letter Sigma). By calculating the standard deviation, we can see that a set of data is too dispersed if the standard deviation is too high. A set of data is more cohesive or consistent if the computed standard deviation is low.

The formula for standard deviation is: σ = √[ { (x - x1)2 + (x - x2)2 + …. + (x - xn)2 }/ n ]

where x is the mean of the set of data, x1 .. xn are the elements of the set of data itself, and n is the number of elements in the set of data.

From the formula we can say that the standard deviation is the square root of the averages of the squares of the difference between each element and the mean of the set.

After watching this video lesson, we can see that computing for the standard deviation is very effective especially when we need to compare different sets of data. An effective tool indeed for market research, academic thesis or dissertation and business proposals.

Summarize, represent, and interpret data on a single count or measurement variable

CCSS.MATH.CONTENT.HSS.ID.A.2

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Exercises in this Practice Problem
Calculate the standard deviation for Martin McTry.
Explain the elements in the standard deviation formula.
Calculate the standard deviation for the scoring.
Compare the standard deviation of each player with each other.
Compare the results of the two players.
Determine the standard deviation for each set of scores.