Question
If a student scored 12 on a test, of which the mean is 16 and the standard deviation is 4, what is his z-score?
The correct answer is
-1
Calculating Student Z-Score
The z-score measures how many standard deviations a specific data point is away from the mean. It is calculated using the formula:
$ z = \frac{X - \mu}{\sigma} $
Where:
- $X$ is the individual score (12)
- $\mu$ is the mean score (16)
- $\sigma$ is the standard deviation (4)
Applying the Z-Score Formula
Substitute the given values into the z-score formula:
$ z = \frac{12 - 16}{4} $
First, calculate the difference between the score and the mean:
$ 12 - 16 = -4 $
Next, divide this difference by the standard deviation:
$ z = \frac{-4}{4} $
$ z = -1 $
The student's z-score is -1. This means the student scored 1 standard deviation below the mean.
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Important Questions from Measurement and Analysis of Data - Teaching
- Identify the variables that pertain to interval scale of measurement
A. gender
B. date of birth of a person
C. religion
D. time of the day
Choose the correct answer from the options given below: - F-ratio is
- Which statements of the following are true about Spearman-Brown prophecy formula?
A. In the split half method, the reliability coefficient of the whole test can be estimated with the help of
reliability coefficient of the half test by using this formula.
B. This formula may be used to estimate the reliability of ratings as well as test scores.
C. It cannot be used to estimate the reliability of paired comparisons.
D. It cannot be used to obtain the effect on reliability by lengthening or repeating a test.
Choose the correct answer from the options given below: - Which of the following is NOT true about errors in measurement?
- In a two-tailed test, for a particular degree of freedom, if a null hypothesis could not be rejected at 0.01 level of significance, then at 0.05 level of significance, this null hypothesis
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