1.7.A—Calculate measures of center and position for quantitative data

Calculate measures of center and position for quantitative data.

• Two commonly used measures of center in the distribution of a quantitative variable are the mean and median.
• The mean is the sum of all the values divided by the number of values and can be found with and without using technology. For a sample, the mean is denoted by x-bar: 1xx= ∑n i i=1 n , where xi represents the ith data point in the sample and n represents the number of data values in the sample.
• The median is the middle value when the data set is ordered from smallest to largest and can be found with and without using technology. One common method for determining the median of a data set with an even number of values is to use the mean of the two middle values. A common method for determining the median of a data set with an odd number of values is to use the value in the middle of all the values.
• In an ordered data set, the smallest value is the minimum value, and the largest value is the maximum value.
• The first quartile, denoted by Q1, is the median value of the lower half of the ordered data set from the minimum value to the position of the median. Approximately 25% of the values in the data set are less than or equal to Q1. The third quartile, denoted by Q3, is the median value of the upper half of the ordered data set from the position of the median to the maximum value. Approximately 75% of the values in the data set are less than or equal to Q3. The second quartile, Q2, is also the median of the data set. Q1 and Q3 form the boundaries for the middle 50% of values in an ordered data set.
• The pth percentile is the value that has p% of the data less than or equal to it when the data set is ordered from smallest to largest. The first and third quartiles are the 25th and 75th percentiles, respectively.