# How to Plot a Density Histogram

Written by timothy haglund
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When you encounter continuous variables, it is often best to display your data through a histogram. Continuous variables are those which can theoretically take on an endless possibility of values, such as weight. The advantage of plotting a density as opposed to a relative frequency histogram is that a density histogram can reveal probability if the histogram has a large enough sample and small enough cells. This process does not take much work and can tell you much more about your data.

Skill level:
Moderately Easy

### Things you need

• Data set
• Paper
• Pen or pencil

## Instructions

1. 1

Take the data from your sample and plot it in a relative frequency histogram. Imagine that the data pertains to the birth weight of 100 babies born at a local hospital. The x-axis of your histogram will be reserved for weight, while the y-axis will measure relative frequency. Beginning with 0 at the x-y intersect, create a series of hash marks evenly distributed to set apart your cells. Each successive cell will designate an increase of 56.7gr; hence there will be 8 cells within each pound. Label the weight of each cell. On the y-axis, create four hash marks evenly distributed in intervals of .25 and label them so that 0 is at the intersect and 1 is at the highest hash mark.

2. 2

Plot the data. If there are 30 babies whose birth weights fall into the cell which contains weights between 2.72 Kilogram and 2.72 Kilogram 56.7gr, for example, the top of the bar should align with a relative frequency of .3 on the y-axis.

3. 3

Convert your histogram to a relative frequency density histogram by rescaling. To do this, use the equation for relative frequency density:

Relative frequency density = relative frequency / cell width.

Hence, in the example RFD = relative frequency / 8. Now the cells should be the same width, but eight times taller than in the first iteration of your histogram. Whereas the sum of the bar heights was equal to one in the first iteration, now the area of the bars is equal to one in your relative frequency density histogram.

#### Tips and warnings

• In your relative frequency density histogram, some of the bars may (and likely should) go above the 1 mark on the y-axis. The larger your sample size and the smaller your cell width, the more your histogram will come to resemble a curve, called the probability distribution.

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