Measures of Central Tendency Mode Median Mean

The Mode the value or property that occurs most frequently in the data

Find the mode: 6, 7, 2, 3, 4, 6, 2, 6 The mode is 6.

Find the mode: 6, 7, 2, 3, 4, 5, 9, 8 There is no mode for this data.

The Median the central value of an ordered distribution

To find the median of raw data: Order the data from smallest to largest. For an odd number of data values, the median is the middle value. For an even number of data values, the median is found by dividing the sum of the two middle values by two.

Find the median: Data:5, 2, 7, 1, 4, 3, 2 Rearrange:1, 2, 2, 3, 4, 5, 7 The median is 3.

Find the median: Data:31, 57, 12, 22, 43, 50 Rearrange:12, 22, 31, 43, 50, 57 The median is the average of the middle two values =

The Mean The mean of a collection of data is found by: summing all the entries dividing by the number of entries

Find the mean: 6, 7, 2, 3, 4, 5, 2, 8

Sigma Notation The symbol  means “sum the following.”  is the Greek letter (capital) sigma.

Notations for mean Sample mean “x bar” Population mean Greek letter (mu)

Number of entries in a set of data If the data represents a sample, the number of entries = n. If the data represents an entire population, the number of entries = N.

Sample mean

Population mean

Resistant Measure a measure that is not influenced by extremely high or low data values

Which is less resistant? Mean Median The mean is less resistant. It can be made arbitrarily large by increasing the size of one value.

Trimmed Mean a measure of center that is more resistant than the mean but is still sensitive to specific data values

To calculate a (5 or 10%) trimmed mean Order the data from smallest to largest. Delete the bottom 5 or 10% of the data. Delete the same percent from the top of the data. Compute the mean of the remaining 80 or 90% of the data.

Compute a 10% trimmed mean: 15, 17, 18, 20, 20, 25, 30, 32, 36, 60 Delete the top and bottom 10% New data list: 17, 18, 20, 20, 25, 30, 32, 36 10% trimmed mean =