CHAPTER 11: RATIOS Flashcards
Expresses the size of one measure (number x) with respect to the size of another measure (number y)
Ratio
x:y is expressed as…
“x is to y”
When the measure x is divided by the measure y
Ratio to one
the measure y in the denominator is referred to as…
“base”
The relationship of x to y expressed as ratio to any number such as 10 or 100
Percentage
A ratio that expresses the size of a part in relation to the size of the total collection which includes that part
Proportion or Distribution Ratio
A ratio that expresses the size of a part in a collection to another part in the same collection
Interclass Ratio
A ratio that specifically refers to the measure of one variable considered in relation to one unit of a different variable
Rate
A ratio that expresses the value in a time series in terms of the value in another time period called the “base period”
Simple Relative
Simple relative when the base period is fixed and expressed in percentage
Percent Relative Series
Measures the absolute change in percent relatives and is affected by the base period
Percentage Points of Change
Measures the relative change in percent relatives and is NOT affected by the base period
Percent Change
Simple relative when the base period is the preceding year so that the base period moves and expressed in percentage
Link Relative Series
The simple relative in period b with respect to period a, denoted by _________, is defined as __________
P a|b, P a|b = P b/P a
Property that implies that the simple relative for a given period with respect to the same period is 1 or 100%
Identity Property: P a|a = 1
Property that implies that if two periods are interchanged, the corresponding simple relatives are reciprocals of each other
Time-Reversal Property: P a|b P b|a = 1 or P a|b = 1/P b|a
Identify the property:
P a|b P b|c P c|a = 1
Circular Property
Identify the property:
P a|b P b|c = P a|c
Modified Circular Property
Change that is measured in terms of the unit used to measure the two quantities
Absolute Change
Change that is often expressed in percentage
Relative Change
Averaging of ratio where the ratio with the largest base is given the greatest importance
Weighted Mean
Averaging of ratios where all values are given the same weights
Simple Arithmetic Mean
The average of a collection of measurements consisting of ratios wherein the ratios with larger bases are given heavier weights
Ratio of Sums or Means (R)
An averaging link relative that is defined only for data sets that contain positive observations where for any set of n positive numbers and is defined as the nth root of their product
Geometric Mean (G)
An averaging rate where for any set of n positive integers it is given by the reciprocal of the arithmetic mean of the reciprocals of the observations
Harmonic Mean (H)
Can be used as a measure of central tendency when a data set contains values that represent rates that all have the same number of units in the numerator
Harmonic Mean (H)
Values of a variable arranged in a time sequence
time series
What are the advantages of ratio to one?
- Easier to work with small numbers rather than large numbers
- Facilitates the comparison of different ratios when their bases are all equal to 1
The base period is usually identified for reporting purposes as…
“base period = 100”
