Which of the following is not a measure of dispersion?. a) The range. b) The 50th Percentile. c) The standard deviation. d) The interquartile range
The correct answer is b) The 50th Percentile
The correct answer is b) The 50th Percentile.
Measures of dispersion quantify the spread or variability of data values in a data set. They provide information about how spread out the data points are and help to identify the degree of variability within the data set.
a) The range: This measure calculates the difference between the maximum and minimum values in a data set. It gives a clear indication of how spread out the data values are.
Example: For the data set {2, 5, 7, 9}, the range is 9 – 2 = 7.
c) The standard deviation: This measure calculates the average deviation of data points from the mean. It takes into account the deviation of each data point and provides a more precise measure of dispersion.
Example: For the data set {2, 5, 7, 9}, the standard deviation is approximately 2.943.
d) The interquartile range: This measure calculates the difference between the third quartile (75th percentile) and the first quartile (25th percentile). It gives a measure of the spread of the middle 50% of the data, which is helpful in identifying outliers or extreme values within the data.
Example: For the data set {2, 5, 7, 9}, the first quartile is 3.5 and the third quartile is 7.5. Therefore, the interquartile range is 7.5 – 3.5 = 4.
b) The 50th Percentile (also known as the median): This measure represents the middle value in a data set when arranged in ascending or descending order. While it provides information about the central tendency of the data, it does not measure the dispersion or variability of the data set.
Example: For the data set {2, 5, 7, 9}, the 50th percentile is 6.
In summary, the 50th percentile (b) is not a measure of dispersion, whereas the range (a), the standard deviation (c), and the interquartile range (d) all provide information about the spread or variability of a data set.
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