Section 2.4 notes Measures of Center Statistics Section 2.4 notes Measures of Center

A measure of center is a value at the center or middle of a data set. The mean of a set of values is obtained by adding the values and dividing by the total number of values.

Sample size – the number of values in the data set, denoted by lower case n. The median of a data set is the middle value when the original data values are arranged in ascending (or descending) order.

Odd number of values – median is the number in the exact middle. Even number of values – median is the average (mean) of the two middle numbers.

The mode of a data set is the value that occurs most frequently, denoted by M. bimodal – data set has two modes multimodal – data set has more than two modes A data set can also have no mode.

The midrange is the value that is halfway between the highest and lowest values in the data set. It is found by adding the highest + lowest and then dividing by 2. Round-off Rule – Go one more decimal place than the values in the original set of data.

Example: 18, 16, 23, 25, 19, 18, 20, 38 mean = 177/8 = 22.125 round to 22.1 median = 16, 18, 18, 19, 20, 23, 25, 38 19+20 = 39/2 = 19.5 mode = 18 midrange = 16 + 38 = 54/2 = 27

mean always yes median no mode rarely used How common? Existence Takes every value into account Affected by extreme values Advantage/ Disadvantage mean most familiar always yes used often/affected by extremes median commonly used no good choice if there are extreme values mode Sometimes used might not exist; could be more than one frequently used for qualitative data midrange rarely used not common; sensitive to extremes