Know how many numbers are in your sample. Do the numbers vary across a large range? Or are the differences between the numbers small, such as just a few decimal places? Know what type of data you are looking at. What do your numbers in your sample represent? this could be something like test scores, heart rate readings, height, weight etc. For example, a set of test scores is 10, 8, 10, 8, 8, and 4.
The mean is the average of all your data points. This is calculated by adding all of the numbers in your sample, then dividing this figure by the how many numbers there are in your sample (n). In the sample of test scores (10, 8, 10, 8, 8, 4) there are 6 numbers in the sample. Therefore n = 6.
For example, use the data set of quiz scores: 10, 8, 10, 8, 8, and 4. 10 + 8 + 10 + 8 + 8 + 4 = 48. This is the sum of all the numbers in the data set or sample. Add the numbers a second time to check your answer.
In the sample of test scores (10, 8, 10, 8, 8, and 4) there are six numbers, so n = 6. The sum of the test scores in the example was 48. So you would divide 48 by n to figure out the mean. 48 / 6 = 8 The mean test score in the sample is 8.
This figure will give you an idea of how far your data is spread out. Samples with low variance have data that is clustered closely about the mean. Samples with high variance have data that is clustered far from the mean. Variance is often used to compare the distribution of two data sets.
For example, in our sample of test scores (10, 8, 10, 8, 8, and 4) the mean or mathematical average was 8. 10 - 8 = 2; 8 - 8 = 0, 10 - 8 = 2, 8 - 8 = 0, 8 - 8 = 0, and 4 - 8 = -4. Do this procedure again to check each answer. It is very important you have each of these figures correct as you will need them for the next step.
Remember, in our sample we subtracted the mean (8) from each of the numbers in the sample (10, 8, 10, 8, 8, and 4) and came up with the following: 2, 0, 2, 0, 0 and -4. To do the next calculation in figuring out variance you would perform the following: 22, 02, 22, 02, 02, and (-4)2 = 4, 0, 4, 0, 0, and 16. Check your answers before proceeding to the next step.
In our example of test scores, the squares were as follows: 4, 0, 4, 0, 0, and 16. Remember, in the example of test scores we started by subtracting the mean from each of the scores and squaring these figures: (10-8)^2 + (8-8)^2 + (10-8)^2 + (8-8)^2 + (8-8)^2 + (4-8)^2 4 + 0 + 4 + 0 + 0 + 16 = 24. The sum of squares is 24.
In our sample of test scores (10, 8, 10, 8, 8, and 4) there are 6 numbers. Therefore, n = 6. n-1 = 5. Remember the sum of squares for this sample was 24. 24 / 5 = 4. 8 The variance in this sample is thus 4. 8.
Remember, variance is how spread out your data is from the mean or mathematical average. Standard deviation is a similar figure, which represents how spread out your data is in your sample. In our example sample of test scores, the variance was 4. 8.
Usually, at least 68% of all the samples will fall inside one standard deviation from the mean. Remember in our sample of test scores, the variance was 4. 8. √4. 8 = 2. 19. The standard deviation in our sample of test scores is therefore 2. 19. 5 out of 6 (83%) of our sample of test scores (10, 8, 10, 8, 8, and 4) is within one standard deviation (2. 19) from the mean (8).
It is important that you write down all steps to your problem when you are doing calculations by hand or with a calculator. If you come up with a different figure the second time around, check your work. If you cannot find where you made a mistake, start over a third time to compare your work.
