Chapter 3: Averages and Variation

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Presentation transcript:

Chapter 3: Averages and Variation Section 1: Measures of Central Tendency

Measures of Central Tendency A number that is meant to convey the idea of a center or a typical value for the data set.

Mode · The data value that occurs the most frequently for a set of data values · Some data sets have no mode · Data sets may have more than one mode .

Median · The middle number for a collection of data values which are in order from least to greatest · the median is not influenced by extreme data values and therefore is a resistant measure

Mean mean = = sum of the data values number of data values population mean represented by · sample mean represented by x The mean is sensitive to outliers and therefore is not a resistant measure; it does not resist the effect of extreme values.

Examples Find the mean and median for the following sets of data. #1 #2 #3 85 105 85 81 81 81 78 78 78 76 76 76 70 70 45

Relationship between mean and median · For a distribution which is skewed to the right, the mean will be greater than the median. · For a distribution which is skewed to the left, the mean will be less than the median. For a bell shaped distribution, the mean and median will be equal.