What is a standard score? How do you find the standard score for a particular data value?
A standard score, also known as a z-score, is a statistical measure that represents the number of standard deviations a given data value is from the mean of a distribution
A standard score, also known as a z-score, is a statistical measure that represents the number of standard deviations a given data value is from the mean of a distribution. It is helpful in comparing and interpreting values in different datasets.
To find the standard score for a particular data value, you need to follow these steps:
1. Calculate the mean (µ) and standard deviation (σ) of the dataset you are working with. These measures describe the average and spread of the data, respectively.
2. Subtract the mean (µ) from the data value you want to find the standard score for. This will give you the deviation from the mean.
3. Divide the deviation by the standard deviation (σ). This will give you the number of standard deviations the data value is away from the mean.
Mathematically, the formula for finding the standard score (z-score) is:
z = (x – µ) / σ
Where:
z = standard score (z-score)
x = data value
µ = mean
σ = standard deviation
For example, let’s say you have a dataset of exam scores with a mean of 80 and a standard deviation of 10. If a particular student scored 90 on the exam, you can calculate their standard score as follows:
z = (90 – 80) / 10
z = 10 / 10
z = 1
In this example, a score of 90 is one standard deviation above the mean of 80. Thus, the standard score (z-score) for this student is 1.
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