2. Basic Math Review
• Introduction
o For most appraisal math, a basic four-function calculator is
recommended.
o The functions on a basic calculator are add ( + ), subtract ( – ),
multiply ( × ), divide ( ÷ ), percent ( % ), and square root ( √ ).
• Decimals, Fractions, and Percentages
o The period that sets apart a whole number from a fractional
part of that number is called a decimal point.
The position of the decimal point determines the value of the
number.
Any numerals to the right of the decimal point are less than one.
The 10th position is the first position to the right of the decimal
point.
The 100th position is the second to the right of the decimal point.
The 1,000th position is the third to the right of the decimal point.
3. Basic Math Review (continued)
• Decimals, Fractions, and Percentages
o Converting Fractions into Decimals
Fractions are always composed of two numbers, one on
top, and one on bottom.
The top number is the numerator, and the bottom number
is the denominator.
These numbers are related as a part to the whole, where
the numerator (top) is the part of the denominator
(bottom) whole.
o Converting Decimals to Percentages
To convert a decimal to a percentage move the decimal
point two places to the right and add a percent symbol.
When no decimal is present (in whole numbers), assume
the decimal is to the very right of the number (for
example, 10 is the same as 10.0).
4. Basic Math Review (continued)
• Decimals, Fractions, and Percentages
o Converting Percentages to Decimals
When working with numbers like 10% or 20%, the decimal
point is assumed to be on the right side of the number.
Move the decimal point two places to the left and remove the
percentage sign.
• Rounding
o Rounding a number means making it the closest whole
number or other designated position, i.e., making 5.8 up to
6 or rounding $392 to the nearest hundred ($400).
o If the number is greater than or equal to half of the place
you are rounding to, round up; if it is lower, round down.
This depends on the position to which you are rounding.
5. Formulas
• Basic Formulas
o Part = Whole x Rate
o Whole = Part ÷ Rate
o Rate = Part ÷ Whole
• Working with Algebra
o The basic algebraic formula is: x (± or ×/÷) y = z.
The key to this principle is that whichever operation is in
the formula, whether it be +, –, ×, or ÷, use the opposing
operation and perform it to both sides of the equals sign (
= ).
6. Area and Volume Calculations
• Linear Measurement
o A linear measurement is a measurement of distance and can
be straight, curved, or angled.
• Area Measurement
o When a second dimension is included, the measurement
becomes an area measurement instead of a linear one.
o Area articulates the amount of space covered, whether by a
real object or theoretical shape, and is always expressed in
terms of square measurements.
• Volume Measurement
o When a third dimension is added, volume is being
quantified, that is the amount of space being occupied.
7. Area and Volume Calculations (continued)
• Volume Measurement
8. Area and Volume Calculations (continued)
• Conversions
9. Area and Volume Calculations (continued)
• Area of Odd Shapes
o Unfortunately, lots and rooms are not always perfect
rectangles, and warehouses and other industrial
buildings are not always perfect cubes or rectangles.
o When you have to calculate area for an irregular lot or
building, break it down into its component parts.
• Volume of Odd Shapes
o Break the object into its simpler component parts and
determine the volumes separately before you add them
all together for a final computation.
10. Statistics
• Terminology
o Statistics is the science of gathering, categorizing and
interpreting data.
o Population—the entire group (aggregate) of items from
which samples are drawn.
o Parameter—a single number or attribute of the
individual things, persons, or other entities in a
population.
o Sample—a subset of a population.
o Variate—a single item in the group.
o Aggregate—the sum of all individual variates.
11. Statistics
• Measures of Central Tendency
o Central tendency is the numeric value that is
suggested as a typical value in a statistical sample.
o Mean
The mean, commonly known as the average, is calculated
by adding all of the variates together and then dividing
that by the number of variates.
Steps to Calculate Mean
• Array the numbers
• Add all of the numbers
• Divide the total by how many numbers are in the array
12. Statistics (continued)
• Measures of Central Tendency
o Median
The second measure of central tendency is called the
median, which provides a figure that is directly in the
middle of the population.
Steps to Calculate Median
• The number in the middle is the median is the midpoint.
• In situations with an even number of variates, find the
mean of the two numbers on either side of the midpoint.
13. Statistics (continued)
• Measures of Central Tendency
o Mode
The mode is the number that occurs the most frequently,
and when analyzing comparable sales, the most frequently
occurring sales price definitely warrants consideration.
• Measures of Dispersion
o Range
The range is simply the difference between the highest
and lowest variate.
The lower the range, the more clustered the grouping, and
conversely, the higher the range, the more spread out they
are.
14. Statistics (continued)
• Measures of Dispersion
o Average Deviation
All of these variates differ from the central tendency to some
degree; and average deviation measures their combined
average dispersion. For this, the mean is needed.
Once the mean of the sample is known, add the difference of
each variate in relation to the mean together and then divide
the sum by the number of variates in the sample.
o Standard Deviation
Squaring a number means multiplying the figure by itself.
• Once the deviations are squared, the square root (√) of their
mean is taken, and that figure represents the standard
deviation of the sample.
• A square root is, it is the inverse of squaring.
