The Practically Cheating Statistics Handbook, The Sequel! (2nd Edition)

There are some elements from basic math and algebra classes that are must-knows in order to be successful in statistics. This section should serve as a gentle reminder of those topics.

1. How to Convert From a Percentage to a Decimal

Percent means how many out of one hundred. For example, 50% means 50 out of 100, 25% means 25 out of 100.

Step 1: Move the decimal point two places to the left.

Example: 75% becomes .75%.

Step 2: Remove the % sign.

.75% becomes .75.

2. How to Convert From a Decimal to a Percentage

Step 1: Move the decimal point two places to the right:

.75 becomes 75.00

Step 2: Add a % sign.

75.00 becomes 75.00%

Step 3 (Optional): You can drop the zeros if you want

75.00% becomes 75%

3. How to Round to X Decimal Places

Sample problem: Round the number .1284 to 2 decimal places

Step 1: Identify where you want the number to stop by counting the number starting from the decimal point and moving right. One point to the right for the number .1284 would stop between the numbers 1 and 2. Two decimal places for the number .1284 will stop the number between 2 and 8:

.12|84.

Step 2: If the number to the right of that stop is 5 or above, round the number to the left up. In our example, .12|84, the 8 is larger than 5, so we round the left number up from 2 to 3:

.12|84 becomes .13|84.

Step 3: Remove any digits to the right of the stop:

.13|84 becomes .13.

Tip: Another way of looking at this is to take both numbers, either side of that stop mark I put in: 2|8 (we can forget the 4 at the end, as we’re rounding way before that). Think of this as the number 28 and ask yourself: is this closer to 20, or closer to 30? It’s closer to 30, so you can say .12|84, rounded to 2 decimal places, equals .1300. Then, you can just drop the zero.

4. How to Use Order of Operations

In order to succeed in statistics, you’re going to have to be familiar with Order of Operations. The operations: addition, multiplication, division, subtraction, exponents, and grouping, can be performed in multiple ways, and if you don’t follow the order, you’re going to get the problem wrong. For example:

4 + 2 × 3

…can equal either 18 or 10, depending on whether you do the multiplication first or last:

4 + 2 × 3

6 × 3

18 (Wrong!)

4 + 2 × 3

4 + 6

10 (Right!)

Here’s how to get it right every time with an acronym: PEMDAS.

The acronym PEMDAS actually stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, but you may easily remember it as Please Excuse My Dear Aunt Sally. Let’s say we have a question that asks you to solve the following equation:

1.96 + z

Where z =

You are given:

= 5

μ= 3 × 7

s = 5²

n = 100

Step 1: Insert the numbers into the equation:

1.96 + z = 1.96 + ((5 – (3 × 7)) / (5² / √100))*

Or

1.96 + z = 1.96 + ((5 – (3 × 7)) / 5² / 10))**

Step 2: Parentheses. Work from the inside out if there are multiple parentheses. The inside parentheses is 3 × 7 = 21, so:

1.96 +z = 1.96 + ((5 – 21) / (5² / 10))

and there’s only one operation left inside that first set of parentheses, so let’s go ahead and do it:

1.96 + z = 1.96 + ((-16) / (5² / 10))

Next, we tackle the second set of parentheses.

Step 3:Exponents. 5² = 25, so:

1.96 + z = 1.96 + (-16 / (25 / 10))

Step 4: There’s no Multiplication in this equation, so let’s do the next one: Division. Notice that there are two division signs. You may be wondering which one you should do first. Remember that we have to evaluate everything inside parentheses first, so we can’t do the first division sign on the left until we evaluate (25 / 10), so let’s do that:

25 / 10 = 2.5

1.96 + z = 1.96 + (-16/(2.5))

Now we can do the second division:

-16 / 2.5 = -6.4

1.96 + z = 1.96 + (-6.4)

Step 5: Addition.

1.96 + (-6.4) = -4.44

Step 6: Subtraction. In this case there is nothing more to do, so we’re already done!

This should hopefully jog your memory–PEMDAS and Order of Operations is covered in basic math classes and you should be thoroughly familiar with the concept in order to succeed with statistics.

Notes:

* Notice that I placed parentheses around the top and bottom parts of the equation to separate them. If I hadn’t, the equation would look like this:

z = 5 – 3 × 7 / 52 / √100

which could easily be interpreted (incorrectly) as this:

z = (5 – 3 × 7 / 52) / √100

so use parentheses liberally, as a reminder to yourself which parts of the equation go together.

** √100 = 10. You don’t need PEMDAS to evaluate simple square roots like this one.

5. How to Find the Mean, Mode, and Median

Step 1: Put the numbers in order so that you can clearly see patterns.

For example, let’s say we have:

2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99

The mode is the number that appears the most often. In this case the mode is 44—it appears three times.

Step 2: Add the numbers up to get a total. Example:

2 +19 + 44 + 44 +44 + 51 + 56 + 78 + 86