Chapter 4 - Descriptive Statistics

Parameters

The actual value of a population property, such as the population mean, (mu).

Statistic

A calculated value that can be used to estimate the parameter of interest.

Central Tendency

The value around which observations tend to cluster.

Mode

Another way to describe central tendency of a categorical variable. The most common value. Can be used in a frequency distributio

Proportion

The number of cases of interest divided by the sample size.

Median

The value that has an equal number of items above and below it. The very middle. Useful for ordinal data and measurements.

Mean

An arithmetic average of a set of measurements and is typically taken from a sample to estimate the true population mean. Good for symmetrical, bell-shaped distributions.

Weighted Mean

An average of a set of data arranged in a frequency distribution.

Outliers

Rare observations in the tail of the distribution.

Percentiles

Divide up an ordered array into 100 equal slices.

Quartiles

The 25th, 50th, and 75th percentiles.

First Quartile

Divides the bottom quarter from the top three quarters and is the same as the 25th percentile.

Second Quartile

Divides the the bottom two quarters from the top two quarters.

Third Quartile

Divides the top quarter from the bottom three quarters.

5 Number Summary

Minimum, Q1, Median, Q3, Maximum

Range

The difference between the largest and smallest items in a sample. Expressed in the same units as the original measurement.

Interquartile Range

The difference between the third and first quartiles, representing the spread of the middle 50% of the values in a dataset.

Box-Whisker Plot

Illustrates the locations of the median, interquartile range, the 10th and 90th percentiles, and outliers.

Standard Deviation

A measure of the average amount by which each observation differs from the mean. Good for symmetrical, bell-shaped distributions.

Sum of Squares

When the squared deviates are summed together. The sum of squares is obtained by squaring the difference between each observation and the mean of all of the observations, and then summing the squared differences.

Variance (s²)

If the sum of squares is divided by the number of observations minus one. Represents the average of the squared deviations in the sample.

Coefficient of Variation

Standardizing standard deviation relative to the mean.