Question

The results of a common standardized test used in psychology research is designed so that the population mean is 145 and the standard deviation is 50. A subject earns a score of 155. What is the z-score for this raw score

Answer 1

The value 155 is zero standard deviations from the mean, because x = μ , and therefore z = 0.

What is Standard Deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

The key concept we need to manage here is the z-scores , and we can obtain a z-score using the next formula:

z = (x - μ)/σ      ..............[1]

Where

z is the z-score.

x is the raw score: an observation from the normally distributed data that we want standardize using [1].

μ is the population mean.

σ is the population standard deviation.

These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155.

From the question, we know that:

x = 155.

μ = 155

σ = 50

Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:

z = (x - μ)/σ

z = (155 - 155) / 50

z = 0/50

z = 0

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:  

x = μ

Therefore, z = 0

So, the value 155 is zero standard deviations from the [population] mean.

Learn more about Standard Deviation from:

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