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MEASURES OF MEASURES OF CENTRAL TENDENCYCENTRAL TENDENCY
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• Mean• Median • Mode
These are indices representing the
average or typical score attained by a group of
subjects.
This value must best describe the group and
be a representative of all the observations.
Mean
Scores: 89, 90, 95, 92, 91, 88, 89_X = ∑X/n
Mean = (89 + 90 + 95 + 92 + 91 + 88 + 89)/7
= 634/7
= 90.57
the sum of all scores divided by the total number of cases
_X
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Median
Scores: 89, 90, 95, 92, 91, 88, 89
88, 89, 89, 90 , 91, 92, 95 Mdn = 90
the score located at the middle of the distribution
Arrange the scores in order
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Mode
Scores frequency
89 4
90 2
95 1
92 1
91 1
88 2
Mode = 89
the score with the highest frequency
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Calculate the mean, median and Calculate the mean, median and mode of the following scores:mode of the following scores:
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10 17 1614 31 1032 30 2710 23 2835 20 12
ANSWERS ANSWERS
Median = 20
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101010121416172023272830313235
Mode = 10101010121416172023272830313235315
n = 15
Mean = 315/15
= 21
MEASURES OF MEASURES OF VARIABILITYVARIABILITY
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• It indicates how spread or scatter the scores are in the distribution (measure of dispersion).
Ex: Range, Mean Average Deviation, Variance, SIQR, Standard Deviation
RANGERANGE
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Group A SCORES: 88, 89, 89, 90 , 91, 92, 95
Range = 95 - 88= 7
Group B SCORES: 75, 80, 89, 90 , 90, 92, 95
Range = 95 - 75= 20
the difference between the highest and the lowest score in a distribution•
the most primitive way of determining variability of scores
STANDARD STANDARD DEVIATIONDEVIATION
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the sum of squares of the score deviations from the distribution mean divided by the total number of cases less than 1
s = ∑x2
n – 1 _where ∑x2 = ∑(X – X) 2
Case 1: 4, 9, 7, 9, 10, 25
X x x2
4 -6.7 44.49 Mean = 10.679 -1.7 2.797 -3.7 13.47 s = 269.339 -1.7 2.79 6 – 1
10 -0.7 0.4525 14 205.35 = 53.8764 269.33 s = 7.34
Calculate the standard deviation of the following scores:
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X x x2
88 0.5 0.25 Mean = 87.50
90 2.5 6.25
87 -0.5 0.25
87 -0.5 0.25 s = 13.50
88 0.5 0.25 6 - 1
85 -2.5 6.25 = 2.7525 13.50 s = 1.64
Case 2: Case 2: 88, 90, 87, 87, 88, 8588, 90, 87, 87, 88, 85
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Case 2 Illustration
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X =87.582.58 89.1485.8684.22 90.78 92.42
x 87.5s 1.64
1s 1.642s 3.283s 4.92
In most cases, the standard deviation is used to describe the degree of dispersion, spread or variation of scores in a distribution.
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Calculate the standard deviation of the following scores:Score
s A 6 3Score
s B 2 44 4 6 67 4 6 72 3 7 810 9 3 8
Which group is more scattered?
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Calculate the standard deviation of the following scores:
26 31 32 2441 24 16 4637 42 26 7012 30 37 2810 19 33 18
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Measures of Location
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• decile •quartile
• percentile
Distribution of scores
Percentile Percentile Formula:
xNP =
100 where
x = the desired percentile rank
N = number of cases
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IllustrationIllustrationDetermine the score equivalent to percentile 80 in the following test results.
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45 80 4565 23 6767 43 6687 56 8965 29 7854 88 7652 75 7289 67 5676 34 5589 51 45
Procedures Procedures 1. Arrange the scores in an ascending order
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23 55 7529 56 7634 56 7643 65 7845 65 8045 66 8745 67 8851 67 8952 67 8954 72 89
lowest
highest
Procedures Procedures 2. Compute P80 using the formula.
P = xN/100
= (80)(30)/100= 24 or
P80 is the 24th score in thedistribution.
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23 55 7529 56 7634 56 7643 65 7845 65 8045 66 8745 67 8851 67 8952 67 8954 72 89P80
Procedures Procedures P80 is the 24th score in the distribution
(P80 = 78).
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23 55 7529 56 7634 56 7643 65 7845 65 8045 66 8745 67 8851 67 8952 67 8954 72 89
Thus, if your score is 78, that means you surpassed 79% of the class or 20% have scores higher than you have got.
Decile Decile Formula:
xND =
10 where
x = the desired percentile rank
N = number of cases
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Quartile Quartile Formula:
xNQ =
4 where
x = the desired percentile rank
N = number of cases
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Summary Summary Percentile (divides the
distribution into 100 equal parts)
Decile (divides the distribution into 10 equal parts)
Quartile (divides the distribution into 4 equal parts)
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