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									DEFINITIONS

Mathematical Order of Operations
 Actual
   Parentheses Exponent Multiplication Division Addition Subtraction
 Mnemonic Device, or Memorizing Technique
   Please Excuse My Dear Aunt Sally

  Example: 3-1*2+2^(2/4)

Correlation                      = Measure of common relation between two ranges
                                   Answers are between -1 and 1
                                   Six combinations: HI NEG, MED NEG, LO NEG, LO POS, MED POS, HI POS

Variance                         = Used in determining standard deviation
Standard deviation               = Square root of variance
 In normal dist                    67% of information is one SD before and after mean
                                   95% of information is two SD's before and after mean

Exponential
 Raised to the 2nd power           Squared               32
 Raised to the 3rd power           Cubed                 33
 Raised to the 4th power                                 34
 …                                                 …
 Raised to the nth power                                 3n

  Raised to the 1 over 2 power     Square-root
  Raised to the 1 over 3 power     Cube-root
  Raised to the 1 over 4 power
  …
  Raised to the 1 over n power

PRODUCT                            Finds the product of a range 1,2,3,4,5
POWER                              Finds the power of a number 3 to the 2 power
SQRT                               Finds the squareroot         the square root of 3


AVERAGE FUNCTIONS
Mean                               Adds values in a range, and divides by the number of value
Median                             Puts values in the range in numerical order, and finds the middle value in the range --
                                   if even number of values, finds the mean of the two middle values
Mode                               Most frequent value in a range

Why Mean, Median or Mode?
MEAN: most common; use if values are similar and continuous, and not skewed
 EX: use to find average salary in a country where there are not many very rich people and not many very poor people
 -- where there are about the same amount of people in every salary category
MEDIAN: useful if values are not similar, but continuous
 EX: use to find average salary in a country where there are a few very rich and many poor people
MODE: most useful for \"qualitative\" measurements, non-continuous
 EX: use to find favorite primary color (say, blue=1, red=2, yellow=3)

GEOMEAN                          = Multiplies "n" numbers in a range, and takes the nth root
                                   Used with non-negative, non-zero numbers; usually, percentages (such as Annual
                                   Rate of Growth)
MEAN V. GEOMEAN?          From http://www.math.utoronto.ca/mathnet/questionCorner/geomean.html
 Mean                     If all the numbers in the range were the same, what would the value (average) have
                          to be in order to achieve the same total ?

 Geomean                  If all the numbers in the range were the same, what would the value (average) have
                          to be in order to achieve the same product ?

LN                      = Natural Log: What root of n gives e?
EXP                     = Exponent of e: e raised to n gives what answer?
LOG                     = Log: What root of n gives a number? Number is assumed to be 10 if missing.

Annual Rate of Growth
 Simple
 Using natural logs
 Long-range
                      IN EXCEL




NEG, LO POS, MED POS, HI POS




, and finds the middle value in the range --
  the two middle values




ich people and not many very poor people
ry

and many poor people




; usually, percentages (such as Annual
 questionCorner/geomean.html
me, what would the value (average) have


me, what would the value (average) have
?



 er is assumed to be 10 if missing.
PrtScr: The whole screen
Alt-PrtScr: The active window
NUMBER1          1   98%
NUMBER2          2   78%
NUMBER3          3   57%
NUMBER4          4   79%
NUMBER5          5   82%
NUMBER6          6   68%
NUMBER7          7   55%
NUMBER8          8   42%
NUMBER9          9   95%
NUMBER10        10   40%
COUNT
PRODUCT
MEAN
GEOMEAN

GEOMEAN,
using PRODUCT
and COUNT
MEDIAN
MODE
SQRT
e                             =                 2.7183


LN                        e raised to x gives n? -- we are given "e" and "n", we find "x"
e^x=n
To find: e^x=2.718282                                                     [same as log(2.718282,2.718282)]
  Question: What is the natural log of 2.718282?


To find: e^x=7.389056                                                        [same as log(7.389056,e)]
  Question: What is the natural log of 7.389056?


EXP                       e raised to n gives x? -- we are given "e" and "n", we find "x"
e^n=x
To find: e^1=x
  Question: What is the exponential of 1?


To find: e^2=x
  Question: What is the exponential of 2?


EXP(LN(N)=N
 Question: What is the exponential of the natural log of 99?


LN(EXP(N)=N
 Question: What is the natural log of the exponential of 99?


LOG                           y raised to x gives n? -- we are given "y" and "n", we find "x" -- y is assumed to be 10 if missing.
y^x=n
QUESTION                      FORMULA
What is the logarithm
(log) of 8, with base 2?      2^x=8
What is the log of 16, with
base 2?                       2^X=16
What is the log of 27, with
base 3?                       3^X=27
What is the log of e, with
base e?                       e^X=2.718282
[same as ln(e)]

What is the log of 10?        10^x=10
What is the log of 10, with
base 10?                      same
What is the log of 3?         10^x=3
What is the log of 3, with
base 10?                      same

What is the log of:                        1
                                          10
                                         100
                                        1000
same as log(2.718282,2.718282)]



same as log(7.389056,e)]




n", we find "x" -- y is assumed to be 10 if missing.
                                            SIMPLE                USING NATURAL LOGS
                                   Annual Rate                  Annual Rate
                                   of Growth-  Annual Rate      of Growth-  Annual Rate
Years     GDP      C               GDP         of Growth-C      GDP         of Growth-C
     1999     74.7           51
     2000     76.3          51.6          2.14%
              76.5          51.1          0.26%
              83.6          57.8          9.28%
              84.4          58.9          0.96%
              89.4          60.9          5.92%
              96.6           66           8.05%
              91.3          62.5         -5.49%
Mean Growth                               3.02%
Median Growth                             2.14%
Mode Growth                                #N/A
Geomean Growth                           #NUM!


But, suppose we only have data for years 1999 and 2006 (T1 and T2)?
Or, suppose we are interested in long-term annual growth, not each year, and we don't want to use simple or ln?

Long-range Annual Rate of Growth Formula
         GDP                                                                    C
         ValueT2 =           ValueT1 * (1 + g)^(T2-T1)                          ValueT2        =
want to use simple or ln?



                     ValueT1 * (1 + g)^(T2-T1)

								
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