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**How Math can Help Solve Crimes**

Forensic Math How Math can Help Solve Crimes By: Samantha Edgington

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Feet and Height Do you think your foot length is related to how tall you are? Today you will see what the correlation is between these two variables

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**Correlation tells you about the relationship between two variables**

Correlation tells you about the relationship between two variables. Correlations range between 0 and 1. A strong correlation means two variables are directly related, like how much you eat and how full you are. Strong values are from 0.7 to 1.0. A weak correlation means two variables are not related, like how much you eat and your favorite color. Weak values are usually from 0 to 0.4.

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**Here’s what your chart should look like:**

To test if there is a correlation between foot length and height, you will need to make a chart and graph of your data. Here’s what your chart should look like: Foot length Height 11 in. 60 in.

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**As you can see, the data is scattered everywhere**

After you collect your data, you will plot it on what is called a scatter plot. As you can see, the data is scattered everywhere Height Foot Length

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We draw what is called a best fit line, because it is a line that tries to fit within the bounds of all the data points or is as close to all the points as possible. The line allows us to describe a mathematical equation for the correlation. Height Foot Length

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**Y = 1.6301x – 0.038 Y = -1.6301x – 0.038 Correlation = 0.9721**

Looking at the second graph, we notice the line direction has shifted. Notice how the slope is now negative and the correlation is the same as the first graph. Let’s now examine how best fit lines work in a real-life situation! This first graph shows a positive linear correlation. Notice how the y-direction values increase as you increase in the x-direction. Also notice how the slope is positive in the equation. Best fit lines can have a positive, negative, or no correlation based on the slope of the line. The direction of the line tells you the type of correlation.

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Body Temperature After death, the body can no longer keep the temperature at 98.6°F (37°C). Because we know the equation for temperature decrease in the body, we can find out how long the body has been dead since we found it. The correlation between body temperature and time of death is strongly negative.

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The temperature starts at 37°C, normal body temperature and decreases until room temperature (about 25°C) Y = x Correlation = In order to determine the time of death, you find the temperature measured on the line (or using the equation) and draw a line down to the hours. For example, if the body temperature was 80 degrees F, then time of death is close to 19 hours.

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ACTIVITY!

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