Find and interpret the standardized score (z-score) of an individual value in a distribution of data.
z-score = (value – mean) / standard deviation. If the z-score is x, the value is x standard deviations above/below the mean.
A standardized score, or z-score, is a measure of how many standard deviations an individual value is away from the mean of a distribution of data.
To find the z-score of an individual value, you can use the formula:
z = (x – μ) / σ
where:
– x is the individual value you want to find the z-score for
– μ is the mean of the distribution
– σ is the standard deviation of the distribution
Once you calculate the z-score, its value will tell you how far away the individual value is from the mean in terms of standard deviations. If the z-score is positive, then the individual value is above the mean, and if the z-score is negative, then the individual value is below the mean.
For example, let’s say we have a distribution of test scores with a mean of 75 and a standard deviation of 10. If a student scored 85 on the test, we can find their z-score using the formula:
z = (85 – 75) / 10
z = 1
This means that the student’s score is one standard deviation above the mean. In other words, the student’s score is higher than about 84% of the other scores in the distribution.
Similarly, if a student scored 65 on the test, we can find their z-score using the same formula:
z = (65 – 75) / 10
z = -1
This means that the student’s score is one standard deviation below the mean. In other words, the student’s score is lower than about 84% of the other scores in the distribution.
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