6.3) Measures of Dispersion

The range

The range, the difference between the highest and lowest data values in a data set, indicates the total spread of the data. Range = highest data value - lowest data value

Standard deviation

The standard deviation is found by determining how much each data item differs from the mean. 1. Find the mean of the data items. 2. Find the deviation of each data item from the mean: data item - mean 3. Square each deviation: (data item - mean)^2 4. Sum the squared deviations: ∑(data item - mean)^2 5. Divide the sum in step 4 by n-1, where n represents the number od data items: [∑(data item - mean)^2] / (n-1) 6. Take the square root of the quotient in step 5. This value is the standard deviation for the data set. Standard deviation = √([∑(data item - mean)^2 / (n - 1)]) *The standard deviation of a sample is symboled by s, while the standard deviation of an entire population is symbolized by δ (lowercase sigma). Unless otherwise indicated, data sets represent samples, so we will use s for the standard deviation: s = √[(∑(x-x̅ )^2) / (n-1)] **The computation of the standard deviation can be organized using a table with three columns: Data item x | Deviation: (x-x̅) or (Data Item-Mean) | (Deviation)^2: (x-x̅)^2 or (Data Item-Mean)^2

Measures of dispersion

used to describe the spread of data items in a data set. The two most common measures of dispersion are: range and standard deviation.