2.2 Measures of Central Tendency

Skewing distributions

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Data1-4 -3 -2 -1 0 1 2 3 4

Collection 1 Histogram

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Data1-4 -3 -2 -1 0 1 2 3 4

data_mean = 0.0853496data_median = 0.131873

Collection 1 Histogram

Distributions• The way mean and median compare tells

you about the distribution

• Symmetric distributions: mean and median are roughly the same

•“roughly the same” depends on spread

of data – next class

•Mean = 0.09

•Median = 0.12

Skewed Distributions

• Mean and median are not the same

• The mean is skewed by the outlying data

• Left-skewed– mean < median

• Right-skewed– mean > median

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-3 -2 -1 0 1 2 3 4info2

Collection 1 Histogram

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info-4 -2 0 2 4 6 8 10

Collection 1 Histogram

Examples of Skewed Distributions

• mean = -1.08• median = -1.98

• mean = 1.84• median = 2.40

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info-4 -2 0 2 4 6 8 10

info_mean = -1.08146info_median = -1.97846

Collection 1 Histogram

•mean > median

•Right-skewed10203040506070

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-3 -2 -1 0 1 2 3 4info2

info2_mean = 1.84301info2_median = 2.40437

Collection 1 Histogram

•mean < median

•Left-skewed

Using Fathom to calculate mode

• Create a measure called mode

• Use the following formula:mean(x, rank(x) – uniquerank(x) = max(rank(x) –

uniquerank(x)))

• Why is there no mode function in Fathom/Excel?

• Good question…