Lab 2 central tendency and variability
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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 l.jpg

Lab 2:Central Tendency and Variability


Learning objectives l.jpg
Learning Objectives

  • Describe Central Tendency

    • Hand calculation of Mean, Median & Mode

    • SPSS calculation of Mean, Median & Mode


Learning objectives 2 l.jpg
Learning Objectives (2)

  • Describe Dispersion

    • Calculate range, SD and variance by hand

    • Calculate them with SPSS


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Central Tendency

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

  • The Mode

  • The Median

  • The Mean


The mode defined l.jpg
The Mode Defined

  • The most frequently occurring score or category

  • To calculate: find the most frequently occurring score.


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Calculating the Mode

  • 1122333455555556667789

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

  • What is the mode for these data?

  • 12345677778889


The median defined l.jpg
The Median Defined

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


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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


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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


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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]


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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)


The mean defined l.jpg
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.


Mean defined l.jpg
Mean Defined

  • In the sample, the mean is:

  • In the population, the mean is:


Calculating the mean l.jpg
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


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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


The range l.jpg
The Range

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


Calculating the range l.jpg
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.


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Variance Defined

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

  • The population formula:

  • The sample formula:



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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.



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Calculating the Variance

  • What is the variance of the following distribution?

  • 5 6 7 8 9 10

  • Answer: 2.92


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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.


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Standard Deviation Defined

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


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Standard Deviation Defined

  • The population formula:

  • The sample formula {SPSS uses

    (N-1)}:



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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.


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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)


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Using SPSS

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


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Homework

  • Compute estimates of central tendency.

  • Compute estimates of variability.

  • Explain them.


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