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Comparing Numbers
which have a
Margin of Error

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Comparing Imprecise Numbers -
Comparing Numbers without using a Number Line:

Direct Comparison, without using a number line, has many practical advantages because it does not require a physical drawing.

Although a number line provides a visual model which is easy to understand, it is not feasible to use it in most situations. The following limitations make a number line cumbersome and time consuming to use:
  • There is not enough space to physically plot more than a few numbers on the same line graph (number line).


  • Plotting extremely small numbers, or extremely large numbers, or numbers with completely different orders of magnitude, or numbers which are almost equal may each require dramatically different labeling of scale marks. In addition, each situation may require completely different intervals marked on the number line.
Direct Comparison eliminates the problems listed above. Direct comparison does not require a physical drawing.

Real Numbers are sequential. By comparing place values, any two numbers can be compared directly - once the numbers are written in the same standard notation.


Imprecise Numbers - Comparing numbers which have a margin of error:
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Note: Some numbers represent only an approximation of the actual value. Numbers representing voting polls or engineering measurements are two examples.

To quantify the degree of possible error, Poll numbers are reported along with a margin of error. The margin or error simply means the actual result is somewhere within the range represented by the margin of error.

For example, a poll of likely voters for a ballot proposition might be reported something like this: 35% in favor, with a margin of error of plus or minus 4%. This means that the actual number of voters in favor of the ballot measure lies somewhere between 31% and 39% (35% is half way in between).

Example: Compare the following poll numbers - 35% in favor of candidate "A" and 37% in favor of candidate "B". The margin of error for both polls is plus or minus 3%.

If these numbers are within 6% of one another (3% + 3% = 6%), the poll results actually overlap. It is impossible to tell which number is larger. The results are a statistical tie. (Although it is not necessary to draw a number line, a number line provides a visual picture of the overlap in the poll results for this example.)

(1) Plot the range for both numbers on a number line, then (2) look for any overlap.

Math - Number Line Comparison Number Line

The 4% overlap on the number line shows that both numbers are so close together that the actual value of each could fall anywhere within the same 4% range.

It is impossible to tell which number is larger than the other.

The poll results of 35% and 37% are a statistical tie.





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