A histogram is similar to a bar graph but instead displays the frequency of intervals of quantitative variables.

Instructions

1. Split the values of the variable into a set of continuous intervals of typically equal size.
2. For each interval count the total quantity of occurrences that fit into that interval.
3. Draw bars for each interval whose height is the quantity of occurrences counted before.

Properties

"Modality"

The "modality" of a histogram describe where the peaks occur and are described in 3 main categories:

• Unimodal - One clear peak
• Bimodal - Two clear peaks
• Multimodal - More than 2 clear peaks

Shape

The shape of a histogram describes how the "mass" of it falls, generally the shape can be described as one of the three following categories

• Symmetric - Both the left and right sides are largely mirrors of each other
• Left Skewed - Most of the "mass" is on the right side and then a long smaller left trail
• Right Skewed - Most of the "mass" is on the left side and then a long smaller right trail

Numerically when a histogram is "left skewed", it's median will be much greater than it's mean and conversely if it's "right skewed", it's median will be a lot smaller. If the median and mean are approximately the same the histogram is symmetric.

Centre

The centre of a histogram is the location where the values usually "cluster".

Measures of Centre

Spread

The spread of a histogram describes how far most points usually are from the centre of the histogram.

Outlier

An outlier is a single observation in a histogram that is visibly removed from the main "mass" of observations, in other words it's unusually far from the centre of the histogram.

Example

Construct a histogram of the following numbers:

175, 192, 207, 212, 213, 214, 218, 225, 229, 230, 231, 235, 235, 237, 240, 240, 242, 248, 250, 253, 257, 260, 265, 265