Basic psychology 1 Experimental Design _ Basic Statistics by hcj

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									         Lecture Outline 3

Measures of Central Tendency
    Please note: Not all slides/material from the
lectures are included here. This presents only a
                  detailed outline of the lecture.
Measures of Central Tendency

l   Three main types
    l   Mode
    l   Median
    l   Mean
l   Choice depends upon level of measurement
The Mode
l   The mode is the most frequently occurring value
    in a distribution.
l   Abbreviated as Mo
l   EX: 20, 21, 30, 20, 22, 20, 21, 20 (Mo?)
l   Sometimes there is more than one mode
l   EX: 96, 91, 96, 90, 93, 90, 96, 90
l   Bimodal
l   Mode is the only measure of central tendency
    appropriate for nominal-level variables
The Median             Position of the Mdn

•   The median is the middle case of a distribution
•   Abbreviated as Mdn
•   Appropriate for ordinal or interval level data
•   How to find the median?
    • If even, there will be two middle cases – interpolate
    • If odd, choose the middle-most case
• Cases must be ordered
• Multiple identical values in the middle
    • – Numerical value becomes the median
Example of median: Years in
Marriage
l   1
l   5
         l   What is the median?
l   2        l   odd or even?
l   9
l   13                     Position of the Mdn
l   11
l   4    l   (7+1)/2=4th case
         l   Where is the 4th case?
         l   Sort distribution from lowest to highest
Example of median: Years in
Marriage
l   1
l   2
l   4
l   5*
l   9         l   4th case?
l   11        l   5 years=Mdn
l   13        l   Interpretation?
Example of median with 8 cases
l   1
                l   What is the median?
l   1
l   2               Position of the Mdn
l   2
                l   (8+1)/2=4.5
l   3
                l   Half way between the 4th and
l   4               5th case
l   4           l   Mdn=2.5
l   6           l   2.5 years
                l   Interpretation?
The Mean
l   The mean is
    appropriate for
    interval and ratio level
    variables




           X = raw scores in a set of scores
          N = total number of scores in a set
Calculating the Mean: An
Illustration
Respondent                   X (IQ)
1                              125
2                               92
3                               72
4                              126
5                              120
6                               99
7                              130
8                              100
                           ∑X = 864
Step-by-step Illustration: Mode, Median,
and Mean
Suppose that a volunteer contacts friends on campus collecting for a local
charity. She receives the following donations (in Liras):
         5        10       25        15      18         2     5
                                               25
Step 1: Arrange the scores from highest to lowest.
                                               18
                                               15
                                      Mdn 10
                                                 5
                                   Mo            5
Step 2: Find the most frequent score.            2
         Mo = 5

Step 3: Find the middlemost score.

         Mdn = 10
Step-by-step Illustration: Mode, Median, and Mean
Step 4: Determine the sum of scores.
          25
          18
          15
          10
           5
           5
           2
     ∑X = 80



Step 5: Determine the mean by dividing the
sum by the number of scores.
Comparing the Mode, Median, and
Mean

l    Three factors in choosing a measure of central
     tendency
    1.   Level of measurement
    2.   Shape or form of the distribution of data
    3.   Research Objective
Level of Measurement
Shape of the Distribution
l   In symmetrical distribution – mode, median, and
    mean have identical values
l   In skewed data, the measures of central
    tendency are different
    l   Skewness relevant only at the interval level
l   Mean heavily influenced by extreme outliers
    l   median best measure in this situation
Research Objective

l   Choice of reported central tendency depends on
    the level of precision required.
l   Most published research requires median and/or
    mean calculations.
l   In skewed data, report mean and median together
    to understand where the skew is.
This figure shows the relative positions of the mean and median for
right-skewed, symmetric, and left-skewed distributions. Note that
the mean is pulled in the direction of skewness, that is, in the
direction of the extreme observations. For a right-skewed
distribution, the mean is greater than the median; for a symmetric
distribution, the mean and the median are equal; and, for a left-
skewed distribution, the mean is less than the median.




                           Figure 1

								
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