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Computer Integrated assessment

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.

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Computer Integrated assessment

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  1. Computer Integrated assessment

  2. Computer integrated assessment Normal distribution & z-scores

  3. Normal distribution and z-scores Normal distribution z-scores

  4. Normal distribution • 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. Normal distribution & z-scores

  5. Properties of a normal distribution • 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 f 40 47 54 61 68 75 82 Scores Normal distribution & z-scores

  6. Normal distribution of test scores 70 60 50 40 f 30 20 10 0.13% 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% 0.13% 0 40 47 54 61 68 75 82 -3 SD -2 SD -1 SD M +1 SD +2 SD +3 SD Scores Properties of a normal distribution Normal distribution & z-scores

  7. Normal distribution of test scores 70 60 50 40 f 30 20 10 0.13% 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% 0.13% 0 40 47 54 61 68 75 82 -3 SD -2 SD -1 SD M +1 SD +2 SD +3 SD Scores Properties of a normal distribution • Percentage of scores below 61. • 2 + 14 + 34 = 50% Normal distribution & z-scores

  8. Normal distribution of test scores 70 60 50 40 f 30 20 10 0.13% 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% 0.13% 0 40 47 54 61 68 75 82 -3 SD -2 SD -1 SD M +1 SD +2 SD +3 SD Scores Properties of a normal distribution • Percentage of scores above 61. • 34 + 14 + 2 = 50% Normal distribution & z-scores

  9. Normal distribution of test scores 70 60 50 40 f 30 20 10 0.13% 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% 0.13% 0 40 47 54 61 68 75 82 -3 SD -2 SD -1 SD M +1 SD +2 SD +3 SD Scores Properties of a normal distribution • Percentage of scores between 47 and 61. • 14 + 34 = 48% Normal distribution & z-scores

  10. X - M z = SD z z-score = Obtained raw test score X = Mean of the test scores = M Standard deviation of test scores SD = z-scores • Raw test scores from any distribution can be converted to a common scale. • z-scores can easily be compared. Normal distribution & z-scores

  11. X - M X - M z z = = SD SD • 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. z z = = z z = = z z = = z-scores • John obtained 85% in the first mathematics test and 90% in the second mathematics test. • First mathematics test: Mean = 75%; SD = 10 • Second mathematics test: Mean = 85%; SD = 15 • Calculate the z-scores for John for both tests. First test: Second test: 85 - 75 90 - 85 10 15 10 5 10 15 1 0.333 Normal distribution & z-scores

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