computer integrated assessment
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Computer Integrated assessment. Computer integrated assessment. Normal distribution & z-scores. Normal distribution and z-scores. Normal distribution. z-scores. Normal distribution. The normal distribution is a special kind of symmetrical distribution. - PowerPoint PPT PresentationTRANSCRIPT
ComputerIntegrated
assessment
Computer integrated assessmentComputer integrated assessment
Normal distribution & z-scores
Normal distribution and z-scoresNormal distribution and z-scores
Normal distribution
z-scores
Normal distributionNormal distribution
Normal distribution & z-scores
The normal distribution is a special kind of symmetrical distribution.
The normal distribution is used to make comparisons among scores or other kinds of statistical decisions.
The normal distribution is hypothetical.
No distribution of scores matches the distribution perfectly.
Properties of a normal distributionProperties of a normal distribution
Normal distribution & z-scores
In the curve (normal distribution) below the mean, mode and median coincide.
The mean, mode and median is 61 in the curve below.
The standard deviation in the distribution below is 7.
Normal distribution of test scores
Scores
f
61 68 75 82544740
Properties of a normal distributionProperties of a normal distribution
Normal distribution & z-scores
Normal distribution of test scores
Scores
61 68 75 82544740
f
0
10
20
30
40
50
60
70
M +1 SD +2 SD +3 SD-1 SD-2 SD-3 SD
34.13%34.13% 13.59% 2.14% 0.13%13.59%2.14%0.13%
Properties of a normal distributionProperties of a normal distribution
Normal distribution & z-scores
Normal distribution of test scores
Scores
61 68 75 82544740
f
0
10
20
30
40
50
60
70
M +1 SD +2 SD +3 SD-1 SD-2 SD-3 SD
34.13%34.13% 13.59% 2.14% 0.13%13.59%2.14%0.13%
Percentage of scores below 61.
2 + 14 + 34 = 50%
Properties of a normal distributionProperties of a normal distribution
Normal distribution & z-scores
Normal distribution of test scores
Scores
61 68 75 82544740
f
0
10
20
30
40
50
60
70
M +1 SD +2 SD +3 SD-1 SD-2 SD-3 SD
34.13%34.13% 13.59% 2.14% 0.13%13.59%2.14%0.13%
Percentage of scores above 61.
34 + 14 + 2 = 50%
Properties of a normal distributionProperties of a normal distribution
Normal distribution & z-scores
Normal distribution of test scores
Scores
61 68 75 82544740
f
0
10
20
30
40
50
60
70
M +1 SD +2 SD +3 SD-1 SD-2 SD-3 SD
34.13%34.13% 13.59% 2.14% 0.13%13.59%2.14%0.13%
Percentage of scores between 47 and 61.
14 + 34 = 48%
z-scoresz-scores
Raw test scores from any distribution can be converted to a common scale.z-scores can easily be compared.
z =X - MSD
z = z-score
X = Obtained raw test score
M = Mean of the test scores
SD = Standard deviation of test scores
Normal distribution & z-scores
z-scoresz-scores
John obtained 85% in the first mathematics test and 90% in the second mathematics test.First mathematics test: Mean = 75%; SD = 10Second mathematics test: Mean = 85%; SD = 15Calculate the z-scores for John for both tests.
First test:
z =X - MSD
z =85 - 75
10
z =1010
z = 1
Second test:
z =X - MSD
z =90 - 85
15
z =515
z = 0.333
The z-scores can be compared.John performed better in the first test than second test.The reason: the z-score for John’s second test is lower than the z-score for John’s first test.
Normal distribution & z-scores