Mean, Median, and Mode 3.1 Measures of Central Tendency

Average: one number to represent an entire population Mode the value that occurs most frequently in a data set order the data set when it contains a large number of data values Not very stable (changing one number can change the mode dramatically) Median central value of an ordered distribution equal number of data values above and below it uses position rather than specific value if extreme values of the set change, the median usually does not To find the median: Order the data from smallest to largest Odd number of data values → middle number Even number of data values → sum of middle two values ÷ 2 **If you have a large set of n data values, use (n+1)/2 to find the middle value.

Mean = sum of all data values number of data values

Resistant measure—one that is not influenced by extremely high or low values. Mean is NOT resistant Median is more resistant, but a disadvantage is that it is not sensitive to specific size of data value Trimmed mean—mean of the data values after “trimming” a specified percentage of smallest & largest data values (usually around 5%) More resistant than the mean, but sensitive to specific data values. To find the trimmed mean: 1) Order the data 2) Delete the bottom and top 5% (round to nearest integer) 3) Compute the mean of the remaining 90%

HOMEWORK : Read Sec. 3.1 and do problems on p #2, 6, 7, and 8