The sample mean for a recent introductory psychology test was 78, and the sample variance was 9. If a student received a score of 82, what was this student’s z-score?
Standard deviation = square root of variance.
Z = (score-mean)/SD
To calculate the z-score, we need to know the population mean and standard deviation. However, if we assume that the sample mean is a good estimate of the population mean, and the sample variance is a good estimate of the population variance, we can make an approximation.
First, let's calculate the standard deviation by taking the square root of the variance:
Standard deviation = √(variance) = √(9) = 3
To calculate the z-score, we can use the formula:
z = (x - μ) / σ
where:
x = the individual score (82 in this case)
μ = the population mean (assumed to be equal to the sample mean, which is 78)
σ = the population standard deviation (assumed to be equal to the sample standard deviation, which is 3)
Plugging in the values, we get:
z = (82 - 78) / 3 = 4 / 3 ≈ 1.333
Therefore, the student's z-score is approximately 1.333.
To find the z-score of a student's score, we need to use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the student's score
- μ is the mean
- σ is the standard deviation (square root of the variance)
In this case, we are given the mean (μ = 78) and the variance (9). To find the standard deviation (σ), we take the square root of the variance.
σ = √(9) = 3
Now that we have the mean and standard deviation, we can calculate the z-score for a student's score of 82:
z = (82 - 78) / 3
z = 4 / 3
z ≈ 1.33
Therefore, the z-score for a student who received a score of 82 is approximately 1.33.