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University of Houston *
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3300
Subject
Mathematics
Date
Feb 20, 2024
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2
Uploaded by MajorDonkeyPerson168
To find the raw score, you need more information about the context or the statistical measure
you are referring to. A "raw score" typically means the original, unprocessed data point in a
dataset. If you're dealing with z-scores or standardized scores, you can use the z-score formula
to find the raw score.
### Formula for finding raw score from z-score:
\[ X = Z \times \sigma + \mu \]
Where:
- \(X\) is the raw score,
- \(Z\) is the z-score,
- \(\sigma\) is the standard deviation of the population,
- \(\mu\) is the mean of the population.
### Example:
Suppose you have a z-score of \(2.5\), a population mean (\(\mu\)) of \(50\), and a population
standard deviation (\(\sigma\)) of \(10\). Using the formula:
\[ X = 2.5 \times 10 + 50 = 75 \]
So, a z-score of \(2.5\) in this context corresponds to a raw score of \(75\) in the original data.
If you have more details or a specific scenario in mind, please provide additional information so I
can give a more accurate response.
A person scores 85 on a test of verbal ability and 6.3 on a test of math ability. For the
verbal ability test, the mean for people in general is 45 and the standard deviation is 20.
For the math ability test, the mean for people in general is 0 and the standard deviation
is 7. Which is this person's stronger ability, verbal or math? Explain your answer to a
person who has never had a course in statistics.
how to find z score from this
A Z-score is a measure of how many standard deviations a particular score is from the
mean of a distribution. To find the Z-score for a given score in a distribution, you can
use the formula:
\[ Z = \frac{{X - \mu}}{{\sigma}} \]
Where:
- \( Z \) is the Z-score,
- \( X \) is the individual score,
- \( \mu \) is the mean of the distribution,
- \( \sigma \) is the standard deviation of the distribution.
Let's find the Z-scores for both the verbal and math test scores:
### Verbal Ability Test:
Given:
- \( X_{\text{verbal}} = 85 \) (individual verbal score),
- \( \mu_{\text{verbal}} = 45 \) (mean for verbal test),
- \( \sigma_{\text{verbal}} = 20 \) (standard deviation for verbal test).
\[ Z_{\text{verbal}} = \frac{{85 - 45}}{{20}} = 2 \]
### Math Ability Test:
Given:
- \( X_{\text{math}} = 6.3 \) (individual math score),
- \( \mu_{\text{math}} = 0 \) (mean for math test),
- \( \sigma_{\text{math}} = 7 \) (standard deviation for math test).
\[ Z_{\text{math}} = \frac{{6.3 - 0}}{{7}} \approx 0.9 \]
### Interpretation:
- A Z-score of 2 for verbal ability indicates that the person's verbal score is 2 standard
deviations above the mean for people in general.
- A Z-score of 0.9 for math ability indicates that the person's math score is 0.9 standard
deviations above the mean for people in general.
### Conclusion:
The person's verbal ability is relatively stronger compared to their math ability. This
conclusion is based on the fact that the Z-score for verbal ability is higher (2) compared
to the Z-score for math ability (0.9). In a standardized distribution, a higher Z-score
indicates a more exceptional performance relative to the mean of that distribution.
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