You are watching: Distance between numbers on a number line

The number line is the key visual basic in statistics and we regularly want to look at 2 points on the number line and determine the distance between them. This is supplied to find the basic of a rectangle or one more figure the lies above the number line. Through the end of this section, girlfriend will have the ability to determine the street between any type of two point out on a number heat that originates from a statistics application.

## Finding the Distance between Two Points through Positive coordinates on a Number Line

The key to recognize the distance between two clues is come remember the the geometric meaning of subtraction is the distance in between the two numbers as lengthy as we subtract the smaller sized number native the larger.

Example \(\PageIndex1\)

Find the distance between the points 2.5 and 9.8 together shown below on the number line.

**Solution**

To find the distance, we simply subtract:

\<9.8\:-\:2.5\:=\:7.3 \nonumber\>

Example \(\PageIndex2\)

When finding probabilities involving a uniform distribution, we have actually to uncover the base of a rectangle that lies on a number line. Find the base of the rectangle shown below that to represent a uniform circulation from 2 come 9.

**Solution**

We simply subtract:

\<9\:-\:2\:=\:7 \nonumber\>

## Finding the Distance between Two points on a Number Line once the coordinates Are no Both Positive

In statistics, it is usual to have actually points top top a number line whereby the points are not both positive and also we need to find the distance in between them.

Example \(\PageIndex3\)

The diagram below shows the confidence interval for the difference between the ratio of men who are planning top top going into the health care profession and the ratio of women. What is the broad of the confidence interval?

**Solution**

Whenever we desire want to find the distance in between two numbers, we always subtract. Recall that subtracting a negative number is adding.

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\<0.01\:-\:\left(-0.04\right)\:=\:0.01\:+\:0.04\:=\:0.05 \nonumber\>

Therefore the width of the confidence interval is 0.05.

Example \(\PageIndex4\)

The typical value of credit transaction card account is -6358 dollars. A examine was excellent of current college graduates and also found their average value for their credit transaction card accounts to be -5215 dollars. The number line below shows this situation. How much apart are these values?

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