3.1 Measures of Central Tendency: Mean, Median, and Mode Mode: the value that occurs the most frequently Find the mode 5 3 7 2 4 4 2 4 8 3 4 3 A data set can have two modes. If there are any more than 2 or in some cases 3 data values that occur the most the data has NO MODE Median: Central value of an ordered distribution a. Order data from smallest to largest b. For an ODD number of data values Median= c. For an EVEN number of data values Median = Find the median 19 19 27 28 18 35 6 7 10 3 12 15 8 Mean: Average Mean=Sum of all entries/Number of Entries Formulas for Mean Σx read as “sum of all x” Sigma is the greek letter, it means the sum of whenever you see it. X read as ___________________ µ Greek Letter___________________ Sample Mean: When data is that of a sample Σx
X=
n
Population Mean: When data is for all members of a population Formulas are the same, just what symbol you use is a signal to anyone studying your data how you got it Σx
µ=
N
The capital N, its bigger cause it is WHOLE POPULATION Resistant Measures: measures that are not influenced by _____________________________ _________________________ Mean is ________________________________ Median_________________________________ Find the mean and median of the following data on income of people at a party 55,000 62,000 71,000 74,000 10,000,000 5% Trimmed Mean 1. Order data from smallest to largest 2. Delete the bottom 5% and top 5% of the data values (example 5% or 20 values is ____ value so you would eliminate_____________________________ 3. Compute the mean of the _______________________________ Compute the 5% trimmed mean of the following list of average class sizes at a local college 14 20 20 20 20 23 25 30 30 30 35 35 35 40 40 42 50 50 80 120