Understanding Summary Statistics and Data Visualization

Mean(SD)

A summary statistic appropriate for normally distributed data.

Median(IQR)

A summary statistic appropriate for skewed data or when outliers are present.

Measures of Central Tendency

Mean, Median, and Mode.

Measures of Dispersion

Variance, Standard Deviation (SD), Range, IQR (Q3-Q1), and extremes.

Mean

The average value, or the center of the sample.

Median

The middle value when the data is ordered.

Mode

The most frequently occurring value in a dataset.

Variance

A measure of how far individual values are from the mean on average.

Standard Deviation (SD)

The square root of the variance.

Range

The difference between the maximum and minimum values.

Interquartile Range (IQR)

The difference between the 75th percentile (Q3) and 25th percentile (Q1).

Sample Mean (IQ example)

96

Sample Mean (Body temperature example)

98

Median Calculation (Odd number of values)

Arrange values in order and select the middle value.

Median Calculation (Even number of values)

Take the mean of the two middle values.

Median Weight of Sample

71

Mode of Weight Sample

66 Kg

Range for IQ Values

43

Range for Body Temperature

2

IQR for IQ Values

32

IQR for Body Temperature

1

Larger Variance

Indicates that values are more spread out from the mean.

Smaller Variance

Indicates that values are closer to the mean.

Variance Example

146 Kg squared if total squared deviation = 1314.1 and n = 10.

Common Graphical Summaries

Boxplots and histograms.

Boxplot

Shows Median, IQR, and potential outliers.

Histogram

Shows the frequency distribution of continuous data.