1. Some Basic Math Concepts for Statistics
Soc2205a/b
Some Basic Math Concepts for Statistics

2. Commonly Used Symbols
∑ (summation symbol) = add together all cases following this symbol
Χ = variable name
Χi = each individual variable in a set
Therefore, ∑ Χi means add all Χ variables in the set together.
∑ Χi = (Χ1 + Χ2 + Χ3 + …)

3. More symbols… Χ2 means to square Χ (multiply Χi by itself)
means find the square root of X (use calculator)
∑ Χi2 means square each X and then add together.
(∑ Χi)2 means find the sum of Χ1 + Χ2 + Χ3 … and then square the total.

4. Order of Operations:
This refers to the order in which calculations in an equation should occur….B-E-D-M-A-S
B = anything within Brackets is done first
E = Exponents (i.e. squares or square roots next)
D = Division and Multiplication are done next, in
M the order that they appear in the equation
A = Addition and Subtraction are done last, in
S the order that they appear.

5. Examples for BEDMAS (2 + 2)2 - (4 / 2 + 1) = (4)2 – (2+1) = 13
In an equation that looks like this…
= (6 + 22) / (4 - 2) = 10 / 2 = 5
4 – 2
Or this… (X2 + 2)2 / (X + 2) = 3, where X = 1

6. Decimals
When adding or subtracting decimals, line up the decimals and add or subtract as usual.
When multiplying two decimals, the decimal place in the answer should total the amount of decimal places in both numbers (ie .22 x .2 = .044)
When dividing two numbers with decimals, you must subtract the decimal places of the divisor from the number in the dividend the number needed for your answer (ie .22 / .2 = 1.1)

7. Multiplying or dividing by 0
Any number multiplied by 0 will equal 0.
0 divided by any number will equal 0.
You cannot divide a number by 0. The answer is undefined.

8. Positive and negative numbers
When adding or subtracting positive and negative numbers, move in the appropriate direction along the number line to obtain your answer.
For multiplication or division:
if two numbers have the same sign, your answer will be positive.
if the numbers have different signs, the answer will be negative

9. Rounding Rules
Always use as many decimal places as your calculator can handle.
Round final answer to 2 decimal places, rounding to nearest number – round up if digits to the right of the second decimal are >5 and down if <5.
Engineer’s Rule: When last digit is exactly 5, round the digit before the last digit to nearest EVEN* number (i.e = 1.12 whereas, = 1.14)
The scientific standard is known as “rounding toward even”.

10. Practice
Try questions 1 – 5 at the end of Appendix H in 1e or Prologue in 2/3e and compare your answers to the ones given by Healey.
(find the 2 errors!)