Basic Math, Healey Appendix H
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Transcript Basic Math, Healey Appendix H
Soc2205a/b
Some Basic Math Concepts for Statistics
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 + …)
More symbols…
Χ2 means to square Χ (multiply Χi by itself)
X 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.
Order of Operations:
This refers to the order in which calculations in an
equation should occur….B-E-D-M-A-S
B
E
D
M
A
S
= anything within Brackets is done first
= Exponents (i.e. squares or square roots next)
= Division and Multiplication are done next, in
the order that they appear in the equation
= Addition and Subtraction are done last, in
the order that they appear.
Examples for BEDMAS
(2 + 2)2 - (4 / 2 + 1) = (4)2 – (2+1) = 13
In an equation that looks like this…
6 + 22 = (6 + 22) / (4 - 2) = 10 / 2 = 5
4–2
Or this… (X2 + 2)2 / (X + 2) = 3, where X = 1
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)
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.
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
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. 1.1250 = 1.12 whereas, 1.135 = 1.14)
The scientific standard is known as “rounding toward even”.
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!)