a) What does a z-score indicate? b) What are the three
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Answered question
2021-09-29
1) What does a z-score indicate?
2) What are the three major uses of z-scores with individuals scores?
Answer & Explanation
hesgidiauE
Skilled2021-09-30Added 106 answers
(1) 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.
where, is the mean, is the standard deviation.
(2) 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.
Data set for comparison:
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.
determining relative frequency:
The relative frequency is calculated using the proportion of total area under a standard 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.
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