The mean and deviation let you compare your test score with other students' test scores.
Mean and deviation are fundamental concepts that must be learned to succeed in elementary statistics classes. The mean and deviation provide details about the distribution of data. With the mean and deviation you have a way to evaluate measurements relative to each other. You can also find out how well you did on a test in comparison with others who took the same test.
Formulas
The mean is the sum of a group of numbers divided by the number of numbers in the group. Essentially, it is the average. For example, the sum of the grades of each test that you take divided by the number of tests taken will give you your mean score for the tests taken. In statistics, the mean can refer to an arithmetic mean, as in this definition, or to the geometric mean or root mean square, which are defined with different formulas.
Mean Deviation
The deviation represents how far a data point, such as a score on a test, is from the average score, or mean. If you scored 75 on a test where the mean was 75, your deviation for that test would be 5 points above the mean or average. A deviation is often further qualified with a number that represents the number of scores in a specific deviation (or region). A teacher might list the deviation breakdowns, i.e., the number of students who scored between 70 and 79, 80 and 89 and 90 and 100 on a test. The number of students per deviation can then be averaged to obtain an average deviation, like five students per letter grade (or a deviation per 10 test points).
Sum of the Differences
The sum of the differences between each data value (or test point) taken and the mean is equal to zero. If you take the difference between each test score in your class and the mean for the test, and then add these differences together, the result will always total zero.
Minimum Deviation
The minimum possible value for a deviation is zero. When all of the test scores on a test are exactly the same, the deviation of each test score from the average (mean) is zero. In this case, all of the test scores will have the minimum deviation (i.e., zero). In addition, because all of the deviations are the same, and each of the deviations is zero, the average deviation of all the test scores will also be zero.
Maximum Deviation
The maximum value for a deviation occurs when half of the data points occur at the minimum point in the range of scores and half of the data points occur at the maximum point in the range. This may occur, for example, when half of the class obtains a score of exactly 60 and the other half of the class obtains a score of exactly 80. The deviation from the mean is then one-half the difference between the maximum and minimum scores, or in this case 20 (80 minus 60).
Tags: test scores, average deviation, each test, mean deviation, test score, between each