 # a) What does a z-score indicate? b) What are the three Wierzycaz 2021-09-29 Answered
a) What does a z-score indicate?
b) What are the three major uses of z-scores with individuals scores?

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(a) Explanation of z-score:
The z-score is used to identify the number of standard deviation a data is below or above the mean. In other words, it indicates the position of a particular data value by measuring the distance from the mean. The formula to find a z-score is as follows.
$$\displaystyle{z}={\frac{{{x}-\mu}}{{\sigma}}}$$
where, $$\displaystyle\mu$$ is the mean, $$\displaystyle\sigma$$ is the standard deviation.
(b) Three major uses of z-scores:
The three major uses of z-scores are given as follows:
To describe the relative standing of each score:
Z-score indicates the position of a particular data value in a normal curve from the mean.
The larger the z-score value, the farther the distance of the data from the mean, whereas, the smaller the z-score, the shorter the distance of the data from the mean.
The negative value of z-score indicates that the data is below the mean, whereas, the positive value of z-score indicates that the data is above the mean.
For comparing data set:
The two different distributions of data can be easily compared by transforming the data to z-scores. Thus, it helps to compare the data sets.
Computation of relative frequency:
The relative frequency is computed using the proportion of total area under a normal bell-shaped curve. Based on the position of data on the curve, the proportion of area beyond z-score can be obtained. Thus, the relative frequency will be computed using z-score.