Descriptive Statistics: Definition, Overview, Types, and Examples

 


What Are Descriptive Statistics?

Descriptive statistics are brief informational coefficients that summarize a given dataset, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

Key Takeaways

  • Descriptive statistics summarize or describe the characteristics of a dataset.
  • Descriptive statistics consist of three basic categories of measures: measures of central tendency, measures of variability (or spread), and frequency distribution.
  • Measures of central tendency describe the center of the dataset (mean, median, mode).
  • Measures of variability describe the dispersion of the dataset (variance, standard deviation).
  • Measures of frequency distribution describe the occurrence of data within the dataset (count).

Types of Descriptive Statistics

All descriptive statistics are either measures of central tendency or measures of variability, also known as measures of dispersion.

Central Tendency

Measures of central tendency focus on the average or middle values of datasets, whereas measures of variability focus on the dispersion of data. These two measures use graphs, tables, and general discussions to help people understand the meaning of the analyzed data.

Measures of central tendency describe the center position of a distribution for a dataset. A person analyzes the frequency of each data point in the distribution and describes it using the mean, median, or mode, which measures the most common patterns of the analyzed dataset.

Measures of Variability

Measures of variability (or measures of spread) aid in analyzing how dispersed the distribution is for a dataset. For example, while the measures of central tendency may give a person the average of a dataset, it does not describe how the data is distributed within the set.

So, while the average of the data might be 65 out of 100, there can still be data points at both 1 and 100. Measures of variability help communicate this by describing the shape and spread of the dataset. Range, quartiles, absolute deviation, and variance are all examples of measures of variability.3

Consider the following dataset: 5, 19, 24, 62, 91, 100. The range of that dataset is 95, which is calculated by subtracting the lowest number (5) in the dataset from the highest (100).

Distribution

Distribution (or frequency distribution) refers to the number of times a data point occurs. Alternatively, it can be how many times a data point fails to occur. Consider this dataset: male, male, female, female, female, other. The distribution of this data can be classified as:

  • The number of males in the dataset is 2.
  • The number of females in the dataset is 3.
  • The number of individuals identifying as other is 1.
  • The number of non-males is 4.

 

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