For example, the equation for standard deviation is variance{\displaystyle {\sqrt {variance}}}. Next to that formula, you might want to write the formula for the variance: ∑(X-µ2)/N After you’ve written out the variance formula, note what each component means. ∑ means “sum,” the (X-µ) represents the difference between each term in the set and mean, and that N is the total number of points in the data set.
Even if you have no idea where to start, get your pencil moving and try to get through what you can. That way, if you need to ask for additional help, you can show your professor or tutor what you’ve already done.
If you’re not sure which extra problems you should do, ask your instructor. They can give you additional work from your textbook or workbook, or direct you to where you might find extra problems.
To calculate the mean, add all of the numbers in your data set and divide the sum by the number of numbers in the set. For example, if your data set includes the numbers 2, 4, 6, 8, 10, and 12, the sum of the set is 42. 42 divided by 6 (the number of data points) is 7. 7 is your mean. The median is the just the middle of any set of numbers. So the median of the data set 2, 4, 6, 8, and 10 is 6. If you have an even number of data points, add the 2 middle numbers of divide by 2.
For example, let’s say you and your 3 friends each have a dog, and their heights are 12 in (30 cm), 20 in (51 cm), 16 in (41 cm), and 32 in (81 cm). First, take the mean of their heights by adding all 4 heights together and dividing by 4. In inches, this would be 12 + 20 + 16 + 32, which equals 80. Divide that by 4 (the total number of dogs) to get 20. So the mean of their heights is 20 in (51 cm). Then calculate the variance by subtracting each individual height from the mean and squaring it. So 20 - 12 is 8, and 8 squared is 64. 20 - 20 is 0, and 0 squared is still 0. 20 - 16 is 4, and 4 squared is 16. And 20 minus 32 is -12, and -12 squared is 144. 64 + 0 + 16 + 144 = 224. To get the final variance, divide the sum of the squared differences from the mean (224) by the number of dogs (4). So the variance of this data set is 56.
For example, if the variance of your and your friends’ dogs’ heights is 56, the standard deviation is the square root of 7. 5. You’d round that up to 8. That tells you that, on average, each dog is about 8 in (20 cm) away from the mean of the dogs’ heights.
Your textbook should have detailed instructions on how to calculate points on a normal distribution graph. You can also find resources online, at websites like minitab or MathWorld.
The best study breaks are 15 to 20 minutes long. It gives your brain enough time to disengage a bit, but won’t complete disrupt your studying.
To focus during class, remove any distractions: don’t bring your computer unless you need it, turn off your phone, and try to get a good night’s sleep the night before.
