Understanding Measures of Dispersion | Range, Standard Deviation, and Interquartile Range

Which of the following is not a measure of dispersion?A) The rangeB) The 50th percentileC) The standard deviation D) The interquartile range

The 50th percentile (option B) is not a measure of dispersion

The 50th percentile (option B) is not a measure of dispersion.

Measures of dispersion are used to describe the spread or variability of a set of data. They quantify how far apart the individual data points are from the average or central tendency. There are several common measures of dispersion, which include the range, standard deviation, and interquartile range.

A) The range: This is the simplest measure of dispersion. It is calculated as the difference between the maximum and minimum values in a data set. The range gives an indication of how wide the spread of the data is, but it doesn’t provide information about the distribution or clustering of the data points within the range.

C) The standard deviation: This measure is widely used and provides a more comprehensive understanding of dispersion. It measures how much the individual data points deviate from the mean (average) of the data set. A higher standard deviation indicates a larger spread or variability among the data points.

D) The interquartile range: This measure is based on quartiles, which divide a data set into four equal parts. The interquartile range is the difference between the upper and lower quartiles, representing the range of the middle half of the data. It is less affected by extreme values and outliers, making it useful for analyzing skewed data sets.

The 50th percentile, also known as the median, is not a measure of dispersion but rather a measure of central tendency. It divides the data set into two equal halves, indicating the middle value. While it provides information about the center of the data, it does not convey anything about the spread or variability.

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