The standard deviation measures the spread of data around the mean. A small standard deviation means the values are close to the mean; a large standard deviation means they are more spread out.It is more useful than the range because it uses every value and is less affected by a single outlier.The standard deviation of a sample is calculated using:s = √( Σ(x − x̄)2 ÷ (n − 1) )
where x is each value, x̄ is the mean and n is the number of values.Steps: calculate the mean; subtract the mean from each value; square each difference; add the squares; divide by n − 1; take the square root.Mean values are often shown on a graph with error bars of plus and minus one standard deviation. If the bars for two means overlap, the difference between the means is probably due to chance and may not be significant. If they do not overlap, the difference is more likely to be real, although a statistical test is needed to be sure.
where x is each value, x̄ is the mean and n is the number of values.Steps: calculate the mean; subtract the mean from each value; square each difference; add the squares; divide by n − 1; take the square root.Mean values are often shown on a graph with error bars of plus and minus one standard deviation. If the bars for two means overlap, the difference between the means is probably due to chance and may not be significant. If they do not overlap, the difference is more likely to be real, although a statistical test is needed to be sure.