Measures of Dispersion Quiz

Measures of dispersion help us quantify how spread out or varied the data points are in a dataset. They tell us the extent of differences among individual values within a given distribution.

Range, interquartile range, mean deviation, standard deviation, and quartile deviation are all common measures of dispersion used in statistics.

Absolute measures of dispersion express the spread of data in the same units as the original data, such as dollars, kilograms, or years. Relative measures of dispersion, on the other hand, are dimensionless and show spread relative to the average, often expressed as percentages.

The 'range' is the simplest measure of dispersion, calculated as the difference between the highest and lowest values in a dataset.

The Interquartile Range (IQR) is the range of the middle 50% of data, calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

The Quartile Deviation (QD) is half the interquartile range (IQR), providing a measure of dispersion within the middle half of the data.

The Mean Deviation (MD) is the average of the absolute deviations of all data points from the mean, providing a measure of the average deviation around the center.

The Standard Deviation (SD) is the most commonly used measure of dispersion. It is the square root of the variance, reflecting the typical deviation of data points from the mean.

The spread of data points around an average, indicating how much they vary from the central value.

A statistical measure that describes the extent to which data is spread out or clustered around the average.

The difference between the largest and smallest values in a dataset.

The difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

Half of the interquartile range, representing the average spread of the middle 50% of data.

The average of the absolute deviations of data points from the mean or median.

The square root of the variance, measuring the spread of data around the mean.

The average of the squared deviations of data points from the mean.

A type of dispersion measure expressed as a percentage or coefficient of an absolute measure.

A measure of dispersion expressed in the same units as the original data.

The coefficient of quartile deviation, calculated by dividing the quartile deviation (Q.D.) by the average of the third and first quartiles.

A measure of dispersion that indicates the relative variability of data by dividing the standard deviation by the mean.

A measure of dispersion calculated as the average of the absolute differences between each data point and the mean.

The most common measure of dispersion, representing the average distance of data points from the mean.

A relative measure of dispersion that indicates the spread of data relative to the central value.

The mean absolute deviation (MAD) is a measure of dispersion that calculates the average distance of each data point from the mean, ignoring the sign of the deviations.

It utilizes all observations in the dataset, making it sensitive to the influence of every data point. This makes it more robust to outliers than standard deviation.

It ignores the signs of the deviation, only considering the absolute values which can lead to a less precise measure of dispersion.

The coefficient of mean deviation is a relative measure, showing the relationship between mean deviation and the average from which the deviation is calculated.

A measure of dispersion that calculates the average squared distance between data points and the mean.

Standard Deviation (SD) is the most commonly used measure of dispersion that quantifies the typical distance between individual data points and the mean.

It provides a comprehensive measure of dispersion as it incorporates every data point's influence, making it robust and representative.

Standard deviation is highly sensitive to extreme values (outliers), and its calculation can be complex compared to other measures.

The Coefficient of Variation (CV) is a relative measure of dispersion, which is used to compare the variability of datasets, especially those with different units.

Lower C.V. indicates higher consistency and uniformity, while higher C.V. suggests greater variability and inconsistency.