Download Standard Score Practice Sheet

Standard Score Practice Sheet (not for marks)
1. John obtained a score of 65 on his midterm. The mean was 75 and the standard deviation
was 10. What was his… z-score? T-score? CEEB-score? IQ-score?
2. Mary obtained a score of 35 on a measure of Extraversion. The mean was 50 and the
standard deviation was 10. What was her… z-score? T-score? CEEB-score? IQ-score?
3. Karen obtained a CEEB score of 550. What was her… z-score? T-score? IQ-score?
Consider the following statements. Mark each as True or False.
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Standard scores have predetermined means and standard deviations.
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T-scores have a mean of 50 and a standard deviation of 15.
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IQ scores have a mean of 100 and a standard deviation of 10.
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Z-scores have a normal distribution.
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Standard scores are useful because they have a normal distribution.
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CEEB scores are used on the GRE.
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T-scores are commonly used in clinical settings.
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A z-score of –100 is mathematically impossible.
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The number -.0258 is more likely to be a z-score than a T-score.
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A T-score of 50 is more likely than an IQ score of 90.
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If a set of data has a normal distribution, then a z-score of 3 is more likely than a
T-score of 3.
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A z-score of 3 or higher is unlikely.
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A T-score of 50 or higher is unlikely.
Answers
1. z=-1. T=40, CEEB = 400, IQ = 85.
2. z=-1.5, T=35, CEEB = 350, IQ=77.5
3. z = .5, T = 55, IQ = 107.5
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Standard Score Practice Sheet #2
1. A pretigeous university will only accept students if they get SAT scores in the top 30%.
What should their cut off score be? SAT follow CEEB standard scores. You may assume
that SAT scores have a normal distribution.
2. A school is trying to identify those students who are most likely to need additional help with
their school work, in order to set up a tutoring program. They want to identify those students
whose IQ is in the bottom 25%. What IQ cut-off score should they use?
3. A school counselor is trying to help students understand what a normal IQ is. The counselor
wants to tell students what is the range of IQ’s in the middle 75% of the distribution. What
are the ends of this range?
4. Dr. Barchard is trying to develop a new measure of Emotional Intelligence. To do this, she
will first write 100 new items, each designed to measure emotional intelligence. Then she
will decide which of these items to keep, by comparing these items with scores on an existing
measure of Emotional Intelligence. To do this, she wants to identify those subjects who
score very high or very low on an existing measure of emotional intelligence (the LEAS).
Then, from the 100 new items she wrote, she will select those items where there is a
difference in the means for those people who score high on the LEAS as compared to those
who score low on the LEAS.
The LEAS has scores that range from 0 to 5. The mean is 3.7 and the standard deviation is
.4. What scores should she use to identify the top 33% and bottom 33% of people, on the
LEAS?
Answers
1. z = .52
SAT = 552
2. z = -.67
89.95 or 90
3. mean-to-z is .375 z = 1.15 and –1.15
IQ’s range from 82.75 to 117.25 (or from 83 to 117)
4. smaller portion for .33
z = .44 and -.44
LEAS cut-offs of 3.524 and 3.876
The lower group consists of those people with LEAS scores below 3.524
The upper group consists of those people with LEAS scores above 3.876