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
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∑ (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…
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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:
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This refers to the order in which calculations in an
equation should occur….B-E-D-M-A-S
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B
E
D
M
A
S
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= 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
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(2 + 2)2 - (4 / 2 + 1) = (4)2 – (2+1) = 13
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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
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When adding or subtracting decimals, line up the
decimals and add or subtract as usual.
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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)
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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
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Any number multiplied by 0 will equal 0.
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0 divided by any number will equal 0.
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You cannot divide a number by 0. The
answer is undefined.
Positive and negative numbers
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When adding or subtracting positive and
negative numbers, move in the appropriate
direction along the number line to obtain your
answer.
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For multiplication or division:
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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
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Always use as many decimal places as your
calculator can handle.
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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.
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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)
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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!)
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