1. Measures of Central
Tendency
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MBBS.DPH.FCPS(CM)M.Phil(CM).Dip-Card
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2. Statistics
Measures of Central
Tendency
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3. • Measures of central tendency are scores
that represent the center of the
distribution.
• Three of the most common measures of
central tendency are:
– Mean
– Median
– Mode
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4. Mean
• The most commonly used measure of central
tendency
• When people ask about the “average” of a group
of scores, they usually are referring to the mean.
• The mean is the sum of all the scores in the
distribution divided by the total scores (the
mathematical average).
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5. Mean (con’t)
• Mean of a sample
• Mean of a population
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6. Mean (con’t)
Exam Scores
75 82 72 68 89
X sum all scores
91 78 94 88 75 n = total number of
scores for the sample
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7. Mean (con’t)
Performance and Memory S tudy
2 2 3 3 4 6
5
Frequency
4 4 4 4 1 4
3
0 2
1
0
1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5
Number of Words Recalled
The mean includes the weight of every score.
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8. Pros and cons of using mean
• Pros
– Summarizes data in a way that is easy to understand.
– Uses all the data
– Used in many statistical applications
• Cons
– Affected by extreme values
• E.g., average salary at a company
– 12,000; 12,000; 12,000; 12,000; 12,000; 12,000;
12,000; 12,000; 12,000; 12,000; 20,000; 390,000
– Mean = $44,167
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9. Median
• The middle score of the distribution when all the
scores have been ranked.
• If there are an even number of scores, the median
is the average of the two middle scores.
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10. Median (con’t)
2 Number of Words Recalled in Performance Study
2
3
3
4
4
4
4
4
10
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11. Mode
• The most frequent score in the distribution.
• A distribution where a single score is most frequent has one
mode and is called unimodal.
• A distribution that consists of only one of each score has n
modes.
• When there are ties for the most frequent score, the
distribution is bimodal if two scores tie or multimodal if more
than two scores tie.
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12. DR TAUSEEF JAVED

13. Mode (con’t)
2
2 Number of Words Recalled in Performance Study
3
3
The mode is 4.
4
4
4
4
4
10
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14. Mode (con’t)
72 72 73 76 78
81 83 85 85 86
87 88 90 91 92
This distribution is bimodal.
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15. Red Blue Green Yellow
Yellow Green Blue Red
Green Red Yellow Blue
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16. Red Blue Green Yellow
Yellow Green Blue Red
Green Red Yellow Blue
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17. • Calculations
• Key: dependent measure is reaction time
– Time it takes to say the color
• Determine the mean, median, and mode
of the datasets in the handout.
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18. The best measure of central
tendency depends on….
• The scale of measurement.
• The shape of the
distribution.
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19. Scales of Measurement
• Nominal scale = mode
• Ordinal scale = median
• Interval scale = mean, median,
or mode
• Ratio scale = mean, median, or
mode
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20. Shape of the Distribution
Skew refers to the general shape of a distribution
when it is graphed.
Symmetrical = zero skew
Scores clustered on the high or low end
of a distribution = skewed distribution
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21. Symmetrical Distribution
16
14
Frequency
12
10
8
6
4
2
0
24.5 29.5 34.5 39.5 44.5 49.5 54.5 59.5 64.5 69.5
Scores
The mean, median, and mode are the same.
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22. • The normal distribution is the “ideal”
symmetrical distribution
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23. Distributions that are skewed have one
side of the distribution where the data
frequency tapers off
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24. Skewed Distribution
Positive Skew
12
10
Frequency
8
6
4
2
0
27 32 37 42 47 52 57 62 67 72 77
Scores
Tail points in the positive direction.
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25. Skewed Distribution
Negative Skew
12
10
Frequency
8
6
4
2
0
27 32 37 42 47 52 57 62 67 72 77
Scores
Tail points in negative direction.
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26. The mean will either underestimate or
overestimate the center of skewed
distributions.
Positive Skew Negative Skew
12
12
10 10
Frequency
Frequency
8 8
6 6
4 4
2 2
0
27 32 37 42 47 52 57 62 67 72 77 0
27 32 37 42 47 52 57 62 67 72 77
Scores Scores
Mode Mode
Median Median
Mean Mean
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27. Kurtosis
• Measure of the flatness or peakedness of
the distribution
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