# Percentage point

Last updated

A percentage point or percent point is the unit for the arithmetic difference between two percentages. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). [1] In written text, the unit (the percentage point) is usually either written out, [2] or abbreviated as pp, p.p., or %pt. to avoid confusion with percentage increase or decrease in the actual quantity. After the first occurrence, some writers abbreviate by using just "point" or "points".

## Differences between percentages and percentage points

Consider the following hypothetical example: In 1980, 50 percent of the population smoked, and in 1990 only 40 percent of the population smoked. One can thus say that from 1980 to 1990, the prevalence of smoking decreased by 10 percentage points (or by 10 percent of the population) or by 20 percent when talking about smokers only – percentages indicate proportionate part of a total.

Percentage-point differences are one way to express a risk or probability. Consider a drug that cures a given disease in 70 percent of all cases, while without the drug, the disease heals spontaneously in only 50 percent of cases. The drug reduces absolute risk by 20 percentage points. Alternatives may be more meaningful to consumers of statistics, such as the reciprocal, also known as the number needed to treat (NNT). In this case, the reciprocal transform of the percentage-point difference would be 1/(20pp) = 1/0.20 = 5. Thus if 5 patients are treated with the drug, one could expect to cure one more patient than would have occurred in the absence of the drug.

For measurements involving percentages as a unit, such as, growth, yield, or ejection fraction, statistical deviations and related descriptive statistics, including the standard deviation and root-mean-square error, the result should be expressed in units of percentage points instead of percentage. [ citation needed ] Mistakenly using percentage as the unit for the standard deviation is confusing, since percentage is also used as a unit for the relative standard deviation, i.e. standard deviation divided by average value (coefficient of variation).

## Related Research Articles

Density is a substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as "y = mx + b" and it can also be found in Todhunter (1888) who wrote it as "y = mx + c".

Taxes and subsidies change the price of goods and, as a result, the quantity consumed. There is a difference between an ad valorem tax and a specific tax or subsidy in the way it is applied to the price of the good. In the end levying a tax moves the market to a new equilibrium where the price of a good paid by buyers increases and the proportion of the price received by sellers decreases. The incidence of a tax does not depend on whether the buyers or sellers are taxed since taxes levied on sellers are likely to be met by raising the price charged to buyers. Most of the burden of a tax falls on the less elastic side of the market because of a lower ability to respond to the tax by changing the quantity sold or bought. Introduction of a subsidy, on the other hand, may either lowers the price of production which encourages firms to produce more, or lowers the price paid by buyers, encouraging higher sales volume. Such a policy is beneficial both to sellers and buyers.

In economics, deadweight loss is the difference in production and consumption of any given product or service including government tax. The presence of deadweight loss is most commonly identified when the quantity produced relative to the amount consumed differs in regards to the optimal concentration of surplus. This difference in the amount reflects the quantity that is not being utilized or consumed and thus resulting in a loss. This "deadweight loss" is therefore attributed to both producers and consumers because neither one of them benefits from the surplus of the overall production.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number, primarily used for expressing proportions, but percent is nonetheless a unit of measurement in its orthography and usage.

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million, parts-per-billion, parts-per-trillion and parts-per-quadrillion. This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.

In economics, elasticity measures the responsiveness of one economic variable to a change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the quantity demanded to fall by 20%. Elasticity in economics provides an understanding of changes in the behavior of the buyers and sellers with price changes. There are two types of elasticity for demand and supply, one is inelastic demand and supply and other one is elastic demand and supply.

A good's price elasticity of demand is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded. Other elasticities measure how the quantity demanded changes with other variables.

The phrase per mille indicates parts per thousand. The associated symbol is , similar to a per cent sign % but with an extra zero in the divisor.

In finance, moneyness is the relative position of the current price of an underlying asset with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification:

In probability theory and statistics, the coefficient of variation (CV), also known as Normalized Root-Mean-Square Deviation (NRMSD), Percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the mean , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in psychology/neuroscience.

Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit. Marginal revenue is the increase in revenue from the sale of one additional unit of product, i.e., the revenue from the sale of the last unit of product. It can be positive or negative. Marginal revenue is an important concept in vendor analysis. To derive the value of marginal revenue, it is required to examine the difference between the aggregate benefits a firm received from the quantity of a good and service produced last period and the current period with one extra unit increase in the rate of production. Marginal revenue is a fundamental tool for economic decision making within a firm's setting, together with marginal cost to be considered.

A basis point is one hundredth of 1 percentage point. The related term permyriad means one hundredth of 1 percent. Changes of interest rates are often stated in basis points. If an interest rate of 10% increased by 1 basis point, it changed to 10.01%.

The percent sign% is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Related signs include the permille sign and the permyriad sign , which indicate that a number is divided by one thousand or ten thousand, respectively. Higher proportions use parts-per notation.

In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual. Supply can be in produced goods, labour time, raw materials, or any other scarce or valuable object. Supply is often plotted graphically as a supply curve, with the price per unit on the vertical axis and quantity supplied as a function of price on the horizontal axis. This reversal of the usual position of the dependent variable and the independent variable is an unfortunate but standard convention.

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably.

A per cent mille or pcm is one one-thousandth of a percent. It can be thought of as a "milli-percent". It is commonly used in epidemiology, and in nuclear reactor engineering as a unit of reactivity.

In chemistry, the mass concentrationρi is defined as the mass of a constituent mi divided by the volume of the mixture V.

Health in Norway, with its early history of poverty and infectious diseases along with famines and epidemics, was poor for most of the population at least into the 1800s. The country eventually changed from a peasant society to an industrial one and established a public health system in 1860. Due to the high life expectancy at birth, the low under five mortality rate and the fertility rate in Norway, it is fair to say that the overall health status in the country is generally good.

## References

1. Brechner, Robert (2008). Contemporary Mathematics for Business and Consumers, Brief Edition. Cengage Learning. p. 190. ISBN   9781111805500. Archived from the original on 18 May 2015. Retrieved 7 May 2015.
2. Wickham, Kathleen (2003). Math Tools for Journalists. Cengage Learning. p. 30. ISBN   9780972993746. Archived from the original on 18 May 2015. Retrieved 7 May 2015.