When a number of people take a test, whether they are students in a class or candidates for a job opening, the average score is an important statistic for those administering the test and those taking it alike. The easiest way to average the score is to add up all the score results and divide by the number of people who took the test. That number is the mean score, and – to most people – the average score, but it isn't the only relevant average. The median score and the mode can both offer useful information, although they aren't as easy to calculate as the mean.
Calculating the Mean Score
If you want to graph a curve based on a set of test results, you need the mean score. It defines the top of the curve and determines which of the people who took the test are "in front" of the curve and which are "behind" it. The process is easy:
- Add the scores of all the people who took the test.
- Divide that total by the number of people.
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Here's an example:
Suppose 10 people take a test that has a maximum score of 100. Their scores are 55, 66, 72, 61, 83, 58, 85, 75, 79 and 67. The total of these scores is 701. Dividing that number by 10 yields an average score of 70.1.
If you want to construct a curve, you plot each score on a graph and, starting from the mean score, draw the lines as equidistant from each point as possible.
An alternative way to calculate the mean is to add up the scores, divide that figure by the total if all the scores were perfect, and multiply by 100 to get a percentage. This type of average won't help place people on a curve, but it's a good determinant of the difficulty of the test. For example, if the above test is scored out of 100, the alternative method to arrive at the average is 701/1000 x 100 = 70.1 percent.
Determining the Median Score
The median score is the one that is exactly in the middle of the set of results. To determine it, you arrange all the scores in order, from lowest to highest. The one that's in the middle is the median score. If the data set is an even number, you might end up with two median scores. Finding the median can be difficult in all but small datasets because there is no easy mathematical formula to calculate it.
Determining the Mode
The mode is useful in large datasets because it's a determination of the score that occurs most frequently. To find it, arrange the scores in order from lowest to highest. Count the number of times each score appears. The one that occurs most frequently is the mode. Depending on the scores, the data may have more than one mode or none at all. The mode is useful because it isn't distorted by values that are extremely small or extremely large.