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Measures of central tendency

Measures of central tendency. The Mean (or Average). The sum of all of the numbers in a set, divided by the number in the set There are 8 students in a class. Grades on the exam were 63, 72, 84, 89, 96, 96, 99, 100 The average is (63+ 72 + 84 + 89 + 96 + 96 + 99 + 100) / 8 = 87.4.

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Measures of central tendency

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  1. Measures of central tendency

  2. The Mean (or Average) • The sum of all of the numbers in a set, divided by the number in the set • There are 8 students in a class. • Grades on the exam were 63, 72, 84, 89, 96, 96, 99, 100 • The average is • (63+ 72 +84 + 89 + 96 + 96 + 99 + 100) / 8 = 87.4

  3. The Median • The middle number in the data set. • The median is the middle value if there are an odd number of cases. • The median is the average of the two middle values if there are an even number of cases. • There are 8 students in a class. • Grades on the exam were • 63, 72, 84, 89, 92, 96, 99, 100 • The median is • (89 + 92) / 2 = 90.5

  4. The Mode • The most frequently occurring value. • There are 8 students in this class. • Grades on the exam were • 63, 72, 84, 89, 96, 96, 99, 100 • The mode is 96

  5. Variance and Standard Deviation

  6. Variance or Dispersion • Variance is the spread about the mean • Why do we care about variance? • Variance in rights protections • Variance in election outcomes • Variance in the presence of genocide across countries • Variance in income inequality • Variance in economic growth • Variance in revolution

  7. Variation • The deviation about the mean Mean

  8. Two sets of numbers X1 = 31 X2 = 7… X = 17 X1 = 24 X2 = 27… X = 23.5

  9. Calculating variance • Square the deviations from the mean, then sum them, then divide by the n (31-17)2 + (7-17)2 + (12-17)2 + (18-17)2 4 Mean of x = 17

  10. The standard deviation • the square root of the variance

  11. Calculating the standard deviation

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