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# Lab 2: Central Tendency and Variability - PowerPoint PPT Presentation

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

• Describe Central Tendency

• Hand calculation of Mean, Median & Mode

• SPSS calculation of Mean, Median & Mode

• Describe Dispersion

• Calculate range, SD and variance by hand

• Calculate them with SPSS

• Central tendency means the middle of the distribution. Three main indicators:

• The Mode

• The Median

• The Mean

• The most frequently occurring score or category

• To calculate: find the most frequently occurring score.

• 1122333455555556667789

• The mode is 5 because there are 7 fives in the distribution.

• What is the mode for these data?

• 12345677778889

• The middlemost score; separates the top 50 % of scores from the bottom 50%

• 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

• 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

• 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]

• 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)

• 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.

• In the sample, the mean is:

• In the population, the mean is:

• 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

• 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

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

• 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.

• The variance is the average or mean of the squared deviations.

• The population formula:

• The sample formula:

• From the last slide, the sum of squared deviations is 8.

• The average is 8/3 = 2.67

• This is the variance.

• What is the variance of the following distribution?

• 5 6 7 8 9 10

• 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.

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

• The population formula:

• The sample formula {SPSS uses

(N-1)}:

• 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.

• 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)

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

• Compute estimates of central tendency.

• Compute estimates of variability.

• Explain them.