Measures of variability, skewness, and kurtosis

Variability

A statistic that describes how spread out data points are within a dataset

Low variability

Close to each other, more consistent

High variability

More spread out data, less consistent

Range

Is a measure of variability that shows how spread out the scores are in a dataset

Range

It calculates the distance between the highest and lowest scores, giving a quick idea of how much participants’ responses vary from one another

Range

Helps in analyzing the information a data set provides, identifying patterns across multiple sets of data, and understanding overall variation

High variability

A large range indicates __

Low variability

A small range indicates __

Interquartile range

Represents the spread of the middle 50% of a dataset, calculated by subtracting the first quartile from the third quartile

Standard deviation

It quantifies the degree of dispersion of the data with respect to the mean

Low standard deviation

The data are closely grouped around the mean, closer to zero

High standard deviation

The data are widely dispersed, far from the zero value

Variance

It is a statistical measure of how far data points spread out from their mean or average

Lower variance

Clustered tightly, more consistent

Higher variance

Wider spread of data, less consistent

Mean absolute deviation

It is the average distance between observations and their mean, it uses the originl units of the data or absolute value, mean deviation

Skewness

Measures the asymmetry of a probability distribution, shows whether the data leans more toward the left or the right of the mean

Positive skewness

The tail is stretched on the right side, most values lie to the left of the mean, less than zero

Negative skewness

The tail is stretched on the left side, move values lie to the right of the mean, greater than zero

Zero skewness

Perfectly symmetrical distribution, mean, median, and mode are approximately equal, equal to zero

Kurtosis

Measures the tailedness of the distribution, provides insights into the likelihood of outliers

Mesokurtic

Normal distribution, moderate tails, equal to three

Leptokurtic

Heavy tails, sharp peak, high probability of outliers, less than three

Platykurtic

Light tails, flat peak, few or no outliers, greater than three

Skewness

Helps determine whether the data is symmetrical or tilted to one side

Kurtosis

Indicates the peakedness and likelihood of extreme values