Finding the Average
Finding the average of something is the calculation you will do the most. To find the average, you sum all the data and divide by the number of data points you added. That’s it.
Formula:
Mean\:(average)=\frac{Sum\:of\:all\:numbers}{How\:many\:numbers\:are\:summed}Example Problem:
\frac{14\:cm\:+\:19\:cm\:+\:12\:cm\:+\:18\:cm\:+\:14\:cm}{5} = 15.4\:cmPercent Change
Bob Bobby and Fred Freddy want to know if a vegan diet or a meat-based diet leads to weight loss. At the start of the vegan diet, Bob Bobby has a mass of 163 lbs. Fred Freddy masses at 218 lbs before he begins the meat-based diet. At the end of the diet, Bob bobby weighs 147 lbs, and Fred Freddy weighs 197 lbs. Who lost more mass?
Fred Freddy because he lost 19 lbs and Bob Bobby lost 16 lbs.
Good. Which diet appears to be better for weight loss?
The meat-based diet.
Are you sure?
Yeah. 19 is greater than 16.
True, but Bobby Bobby lost more mass proportionally.
What???? Are you using magical math?
No, I am using normal math.
Explain.
If Bob Bobby and Fred Freddy had the same mass before the diet, then Fred Freddy’s diet would have resulted in more proportional weight loss. Since the two had different starting masses, the results of the literal weight loss can be misleading.
Huh?
In other words, finding the percentage of lost weight is a better way to present the data than the literal amount.
You’re going to show me some math, aren’t you?
Yep.
Formula:
Percent\:(\%)\:change = \frac{(new\:value - old\:value)}{old\:value} \times 100\%Example Problem #1: Bob Bobby
\frac{(147\:lbs - 163\:lbs)}{163\:lbs} \times 100\%\frac{-16\:\cancel{lbs}}{163\:\cancel{lbs}} \times 100\%-0.1 \times 100\% = -10\%
Example Problem #2: Fred Freddy
\frac{(197\:lbs - 218\:lbs)}{218\:lbs} \times 100\%\frac{-19\:\cancel{lbs}}{218\:\cancel{lbs}} \times 100\%-0.09 \times 100\% = -9\%
As you can see, Bob Bobby lost 1% more mass than Fred Freddy.
Can you have a negative percentage?
Yes. If the new value is less than the old value, then there is a loss of quantity; hence, a negative percentage. If the new value is greater than the old one, there is a quantity gain; thus, a positive percentage.
Percent of a Whole
Let’s say you want to know the percentage of green M&Ms in a bag. To find the percentage, you need to (1) count the number of green M&Ms (part) and (2) the total number of M&Ms (whole), and (3) plug those numbers into the formula below.
Formula:
Percent\:(\%)\:of\:a\:whole = \frac{number\:of\:part}{whole}\times100\%Example:
\frac{14\:green\:M\&Ms}{48\:M\&Ms\:from\:the\:bag}\times100\%= 29\%Therefore, 29% of the M&Ms are green.
Dimensional Analysis
Why dimensional analysis?
Well, the use of DA is for unit conversion. Every unit will have at least one chapter with math that involves unit conversion. The good news is that DA makes unit conversion easy to do.
Most DA you will do is a single unit conversion, the most common being the conversion of inches (in) into centimeters (cm) and pounds (lbs) into kilograms (kg).
68\:\cancel{in}\times\frac{2.54\: cm}{1\:\cancel{in}}= 172.7\:cm150\:\cancel{lbs}\times\frac{1\: kg}{2.2\:\cancel{lbs}}= 69.2\:kgIf you are a Physiology student, unit conversions will get a little bit longer. For example, let’s say you need to convert a 0.9% glucose solution into osmoles. (A 0.9% glucose solution is 0.9 grams of glucose dissolved in 100 milliliters of distilled water.)
\frac{0.9\:\cancel{g}\:glucose}{100\:\cancel{ml}\:H_2O}\times\frac{1000\:\cancel{ml}}{1\:L}\times\frac{1\:\cancel{mole}\:glucose}{180.16\:\cancel{g}\:glucose}\times\frac{1\:Osmol}{1\:\cancel{mole}}= 0.5\:Osmol/L