What is the primary purpose of measures of dispersion in statistics?

Measures of dispersion describe data spread.

• Indicates data variability.

• Highlights extreme values' impact.

• Aids in data comparison.

Fill in the blank: Variance is defined as the average of the squared deviations from the ___.

Mean

True or False: The range of a dataset is calculated by taking the difference between the largest and smallest values.

True

Explain the difference between absolute and relative measures of dispersion.

Absolute vs. Relative Measures of Dispersion

• Absolute measures use same units.

• Examples: range, variance, standard deviation.

• Relative measures allow dataset comparisons.

What does the interquartile range measure?

Measures data spread.

• Focuses on middle 50%.

• Calculates Q3 minus Q1.

• Indicates variability present.

Fill in the blank: The formula for calculating mean deviation involves taking the average of the absolute differences between each value and the ___.

Mean

True or False: The coefficient of variation is calculated by dividing the variance by the mean of the data set.

False. The coefficient of variation is calculated by dividing the standard deviation by the mean.

How is the range for ungrouped data calculated?

The range for ungrouped data is calculated by identifying the smallest and largest values in the dataset and finding the difference between them.

What is the formula for calculating the quartile deviation?

The quartile deviation is calculated as half the difference between the third quartile (Q3) and the first quartile (Q1), expressed as (Q3 - Q1) / 2.

Fill in the blank: The mean deviation is a measure indicating how much the observations in a dataset differ from the ___.

Mean