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Measures of Central Tendency

Measures of Central Tendency. Numbers describing typical data values. The Big Three – Mean, Median & Mode. Mean Most common measure Arithmetic average Statistical symbols. Arithmetic Mean. Population mean Sample mean. Feb. 10. Mar. 9.5. Apr. 7.3. May. 4.8. Jun. 3.

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Measures of Central Tendency

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  1. Measures of Central Tendency Numbers describing typical data values

  2. The Big Three – Mean, Median & Mode • Mean • Most common measure • Arithmetic average • Statistical symbols

  3. Arithmetic Mean • Population mean • Sample mean

  4. Feb 10 Mar 9.5 Apr 7.3 May 4.8 Jun 3 Arithmetic Mean

  5. Median • Median • The middle value, when listed from smallest to largest. • Half of data is above median, half below • With even number of data values, median is half-way between the two central values • 3 5 7 7 9 10 11 33 50 Median = 9 • 3 5 7 9 10 11 33 50 Median = 9.5

  6. Mode • Mode • Value that occurs with greatest frequency • Unimodal • 3 5 8 1 -7 2 5 • Bimodal • 3 5 -7 1 -7 2 5 • Multi-modal • 3 5 -7 1 -7 3 5 • No mode • 3 5 8 1 -7 2 5 • Or • 3 5 -7 -7 3 5

  7. Practice Exercise Consider the following data: 4, -8, 4, -12, 8, 4, -14 What is the value of the mean? What is the value of the median? What (if any) is the value of the mode(s)? What is the range?

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