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Z Score and Distribution

The document discusses standard scores (z-scores) and the normal distribution. It provides examples of calculating z-scores from test scores and using z-scores to find percentages of cases within given ranges in the normal distribution.

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khenliyanah
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39 views13 pages

Z Score and Distribution

The document discusses standard scores (z-scores) and the normal distribution. It provides examples of calculating z-scores from test scores and using z-scores to find percentages of cases within given ranges in the normal distribution.

Uploaded by

khenliyanah
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPTX, PDF, TXT or read online on Scribd
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Standard Score and

Normal Distribution
STANDARD SCORE (Z-score)

A Z-score is a numerical measurement used in statistics of a


value's relationship to the mean (average) of a group of values,
measured in terms of standard deviations from the mean. If a Z-
score is 0, it indicates that the data point's score is identical to
the mean score. A Z-score of 1.0 would indicate a value that is
one standard deviation from the mean. Z-scores may be positive
or negative, with a positive value indicating the score is above
the mean and a negative score indicating it is below the mean.
STANDARD SCORE (Z-
score)
1. Scores on a history test have average of 80 with standard
deviation of 6. What is the z-score for a student who
earned a 75 on the test?

75 -80
Z=
6
Z = -0.83
2. Ariel’s score in there Mathematics test is 42. If the test
has a standard deviation of 10 and a mean of 39. What is
Ariel’s z-score?

42 -39
Z=
10
Z = 0.3
3. A national achievement test is administered annually to
3rd graders. The test has a mean score of 100 and a
standard deviation of 15. If Jane's z-score is 1.20, what was
her score on the test?
x - 100
1.20 =
15
(1.20) (15) = x - 100
18 = x - 100
18 + 100 = x
x = 118
Jane’s score is 118.
Normal Distribution
Distribution
A normal distribution is the proper term for a probability bell curve.
In a normal distribution the mean is zero and the standard deviation is
1. Normal distributions are symmetrical, but not all
symmetrical distributions are normal.
1. Find the percentage of cases falling between z=1.5 and z=2.5.

Add the percentage: 4.4% + 1.7% = 6.1%


2. Find the percentage of cases falling between z = -1.5 and z = 1.5.

Add the percentage: 9.2%+ 15% + 19.1% + 19.1% + 15.0% + 9.2% = 86.6%
3. Find the percentage of cases falling between z = -2.5 and z = 1.

Add the percentage: 1.7% + 4.4% + 9.2% + 15% + 19.1% + 19.1% + 15.0% = 83.5%

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