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Lab 2: Central Tendency and Variability

Lab 2: Central Tendency and Variability. Learning Objectives. Describe Central Tendency Hand calculation of Mean, Median & Mode SPSS calculation of Mean, Median & Mode. Learning Objectives (2). Describe Dispersion Calculate range, SD and variance by hand Calculate them with SPSS.

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Lab 2: Central Tendency and Variability

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  1. Lab 2:Central Tendency and Variability

  2. Learning Objectives • Describe Central Tendency • Hand calculation of Mean, Median & Mode • SPSS calculation of Mean, Median & Mode

  3. Learning Objectives (2) • Describe Dispersion • Calculate range, SD and variance by hand • Calculate them with SPSS

  4. Central Tendency • Central tendency means the middle of the distribution. Three main indicators: • The Mode • The Median • The Mean

  5. The Mode Defined • The most frequently occurring score or category • To calculate: find the most frequently occurring score.

  6. Calculating the Mode • 1122333455555556667789 • The mode is 5 because there are 7 fives in the distribution. • What is the mode for these data? • 12345677778889

  7. The Median Defined • The middlemost score; separates the top 50 % of scores from the bottom 50%

  8. Calculating the Median – Even # of scores • If even number of scores, use the average of two middle scores • 1 2 3 4 5 6 7 8 (Order) • 2 2 3 3 4 5 5 6 (Number) • Median is 3.5 = (3+4)/2

  9. Calculating Median (Even) • 1 2 3 4 5 6 7 8 (Order) • 1 2 2 2 2 3 3 3 (Number) • Median is 2 = (2+2)/2 • 1 2 3 4 5 6 7 8 9 10 (Order) • 1 2 2 5 6 8 9 9 9 10 (Number) • Median is 7 = (6+8)/2

  10. Calculating Median (Odd) • If there are an odd number of scores in the distribution, the median is the middle score [(N+1)/2]. • 1 2 3 4 5 6 7 8 9 (Order) • 1 2 4 5 8 9 9 9 10 (Number) • Median is 8 (fifth score)[(9+1)/2]

  11. Calculating Median (Test) • What is the median? • 1 2 3 4 5 6 7 8 9 (Order) • 2 3 4 5 6 8 9 9 9 (Number) • 1 2 3 4 5 6 (Order) • 0 5 7 9 9 9 (Number)

  12. The Mean Defined • The mean is the arithmetic average. It is the sum of scores divided by the number of scores. • That is, add ‘em all up and divide by how many you’ve got.

  13. Mean Defined • In the sample, the mean is: • In the population, the mean is:

  14. Calculating the Mean • 1 2 3 4 5 • Mean is (1+2+3+4+5)/5 = 15/5 = 3 • 2 2 2 3 3 3 • Mean is (2+2+2+3+3+3) = 15/6 = 2+3/6 = 2.5

  15. Dispersion Defined • Dispersion refers to the spread of scores around the mean. Hug or hate the mean. • Four main indices of dispersion: • Range • Average Deviation • Variance • Standard Deviation

  16. The Range • The Range is the difference between the top and bottom scores (Max – min).

  17. Calculating the Range • What is the range? • 1 2 2 3 3 5 6 7 8 9 • The range is 9-1 = 8. • 5 7 9 12 • The range is 12-5 = 7. • 2 2 2 2 3 3 3 4 4 13 • The range is 13-2 = 11.

  18. Variance Defined • The variance is the average or mean of the squared deviations. • The population formula: • The sample formula:

  19. Calculating the Variance

  20. Calculating the Variance • From the last slide, the sum of squared deviations is 8. • The average is 8/3 = 2.67 • This is the variance.

  21. Calculating the Variance

  22. Calculating the Variance • What is the variance of the following distribution? • 5 6 7 8 9 10 • Answer: 2.92

  23. Calculating the Variance • For reasons we will describe later, SPSS calculates the sample variance like this: • The only difference is (N-1) instead of N. You need this to compare your answer to SPSS. Use N-1 to compare to SPSS so you agree.

  24. Standard Deviation Defined • The standard deviation is the square root of the variance.

  25. Standard Deviation Defined • The population formula: • The sample formula {SPSS uses (N-1)}:

  26. Calculating the SD

  27. A Look Ahead • The mean, variance and standard deviation form the basis of most of the statistics we will be using. • If we do an experiment, we will look at the means and variance to decide if the treatment had an effect.

  28. Review • Here is a distribution: • 2 4 6 6 8 10 • Find the mean, median, mode, range, variance, and standard deviation. • M =6, Med =6, Mo = 6. • Range = 8, V = 6.67 (SPSS=8), SD = 2.58 (SPSS=2.83)

  29. Using SPSS • Next we will wake up SPSS and see how to get it to provide the estimates of central tendency and variability

  30. Homework • Compute estimates of central tendency. • Compute estimates of variability. • Explain them.

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