5.3
z Scores and Unusual Values
z scores are one of the common measures of relative position; they describe the location of a value relative to the mean.
Recall that standardization converts data values into corresponding z scores. Here, the mean always has a zero z score.
A z score of 1 indicates that a data value is one standard deviation above the mean, while minus 2 suggests two standard deviations below the mean.
The ordinary, or majority, of values in any distribution lie within the z score of minus 2 to plus 2. Any values beyond this range are considered unusual, or outliers, and are considered far away from the other data values. Outliers may indicate variabilities in measurement or experimental errors.
For example, a student’s height has a plus 3.3 z score, or 3.3 standard deviations away from the class average, indicating that she is unusually tall for her class.
The z score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. z scores are obtained after the standardization of the values in a dataset. The z score for the mean is 0.
This score indicates how far a value is from the mean in terms of standard deviation. For example, if a data value has a z score of +1, the researcher can infer that the particular data value is one standard deviation above the mean. If another data value displays a z score of -2, one can conclude that the data value is two standard deviations below the mean.
Most values in any distribution have z scores ranging from -2 to +2. The values with z scores beyond this range are considered unusual or outliers. These values lie far from other data points in a distribution. Outliers can occur due to experimental errors and variations in measurement.
For instance, consider a distribution of student heights in a class. After standardization, it is found that one particular student had a z score of +3.3. This means that the student is unusually tall compared to other students in the class.
This text is adapted from Openstax, Introductory Statistics, 6.1 The Standard Normal Distribution
z scores are one of the common measures of relative position; they describe the location of a value relative to the mean.
Recall that standardization converts data values into corresponding z scores. Here, the mean always has a zero z score.
A z score of 1 indicates that a data value is one standard deviation above the mean, while minus 2 suggests two standard deviations below the mean.
The ordinary, or majority, of values in any distribution lie within the z score of minus 2 to plus 2. Any values beyond this range are considered unusual, or outliers, and are considered far away from the other data values. Outliers may indicate variabilities in measurement or experimental errors.
For example, a student’s height has a plus 3.3 z score, or 3.3 standard deviations away from the class average, indicating that she is unusually tall for her class.
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5.3 : z Scores and Unusual Values
Measures of Relative Standing
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5.1 : Review and Preview
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5.2 : Introduction to z Scores
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5.4 : Percentile
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5.5 : Quartile
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5.6 : 5-Number Summary
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5.7 : Boxplot
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5.8 : What Are Outliers?
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5.9 : Modified Boxplots
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