1.7.B—Calculate measures of variability for quantitative data

Calculate measures of variability for quantitative data.

• Three commonly used measures of variability (or spread) in the distribution of a quantitative variable are the range, interquartile range, and standard deviation.
• The range is the difference between the maximum data value and the minimum data value.
• The interquartile range (IQR) is the difference between the third and first quartiles: Q3 − 1.Q
• The standard deviation is a typical deviation of the data values from their mean and can be found with and without using technology. The sample standard deviation is denoted by s and calculated by 1s = ()xx 2 n 1 i −− ∑ , where xi is the data value, x is the mean, and n is the number of data values in the sample. The square of the sample standard deviation, s2, is called the sample variance.