In Math and Science, however, they are slightly different.

ACCURACY has the meaning that I just described: how close a number is to the actual number.

PRECISION, on the other hand, does not refer to how close a number is to an actual number, but rather refers to how many digits and decimal places a number has. (A separate definition for precision also is that it measures how close repeated measurements are to each other, rather than to the actual value.)

As an example, consider a 100 gram block of wood. We are told that this block has a mass of 100 grams. Now, if we put it on balance A, we get a mass of 99.9 grams. When we put it on balance B, we find a mass of 101.350022. We can say that balance A provides us with a more ACCURATE number because it is closer to the known mass of 100 g, but balance B gives us a much more PRECISE number because it displays more decimal places. However, even with the extra decimal places, it isn’t as accurate as balance A. (Maybe there is something wrong with its calibration?)

Do you think that some measurement can be both accurate AND precise? Sure it can.

Let’s suppose we have a bottle of pop. The label says that it is a 1000 mL container. We pour the pop into a graduated cylinder, and determine that there is 998 mL. Since this particular graduated cylinder that we used has no decimal markings, the whole number 998 is as precise as we can get. But that is as precise as the label says. We measure only a 2 mL difference, which isn’t that much (0.2%). So, with this cylinder, we can say that we have a fairly accurate and precise measurement.

If we could determine that the volume in the container was 998.93188 mL, we could say that this number was accurate, and very precise.

Hopefully these examples were able to show you the difference between accuracy and precision. Please comment if you would like some further explanation; this concept always confuses students. I will do my best to clarify.

For any data set, you can perform the analysis to come up with a value for each average. However, here are a few basic guidelines to help you choose the most appropriate form of central tendency to describe your data.

1. For a normal, random distribution of data (evenly distributed), the mean is preferred.

2. For a skewed data set, a median is more appropriate than a mean. The skewed data set (ie. extreme data points) will cause the mean value to be much more extreme than the median, and therefore less central.

3. The mode can be used for non-numerical data. Eg. hair colour in a classroom.

Here are a few examples of where each would be appropriate:

Mean:

1. students’ heights in a classroom
2. temperature over a length of time

Median:

1. income of a group of people
2. test scores for a group of students

Mode:

1. finding the most common hair colour in a room
2. finding the most common car in a parking lot

Hopefully these guidelines will help you to determine which is the most appropriate measure of central tendency to report for your data set.