Percentage point

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The term percentage point is a linguistic aid to denote the absolute difference between two relative figures that are available in percent . Percentage points are mostly used in connection with statistics, for example when comparing election results or economic data.

The designation can be helpful in linguistically clearly distinguishing an absolute comparison of two statements in percentages from the relative comparison. Nevertheless, DIN 5477 recommends avoiding the designation percentage point in order to avoid ambiguities and misunderstandings. Instead, text or formula symbols should be used to clearly distinguish the difference between the ratios and the relative difference.

The term base point is also used, especially in finance . This denotes the hundredth part of a percentage point and is abbreviated with bp , whereas the per ten thousand symbol ‱ is not used in the context of financial mathematics.

Examples

example 1
Suppose the interest rate on savings is increased from 4% to 5%. They say it is increased by one percentage point. Alternatively, it is said to be increased by 25% (based on the previous interest rate).
In this case it would be wrong to say that the interest rate has been increased by 1%. If correctly calculated, the interest rate would then only be 4.04%. On the other hand, it is possible to state that the absolute interest amount (not the percentage interest rate) was increased by 1% of the deposit.
Example 2
A party received 1% of the vote in the first election and 2% of the vote in a second election.
The following statements can be made:
  • The party increased its share of the vote by 100%.
    This is a relative figure for comparing the relative share of votes in the first election and the relative share of votes in the second election. The information refers to the relative share of votes in the first election. Compared to the first election, the relative proportion of votes in the second election was doubled.
  • The party increased its share of the vote by one percentage point.
    This is an absolute indication of the increase in the relative share of votes in the second election, based on the relative share of votes in the first election. The word absolute is to be used with caution here, as it is not about the absolute number of votes.
Example 3
A rental contract contains a clause to adjust the rent as soon as the annual consumer price index with base year 2005 = 100 has changed by more than 4 percentage points up or down within the contract period. The lease was signed in 2008. For 2011 it is now to be checked whether the threshold for an increase or decrease in rent has been reached. The annual consumer price index was 106.6 for 2008 and 110.7 for 2011. The difference in percentage points of the index with base year 2005 = 100 is therefore (110.7 - 106.6 =) 4.1. Therefore, the threshold for a rent increase has been reached or exceeded. If the word “percent” were used instead of “percentage points” in the first sentence of this example, the change would only be rounded to two decimal places (110.7 / 106.6 =) 3.85%. Then there would be no rent increase for 2011.

Mathematical consideration

We consider two parts of an arbitrary ensemble. One is 2%, the other is 3%. Mathematically speaking, the difference between 2% and 3% is a difference of 1% or a factor of 1.5 (based on the first number).

The difference is calculated by subtracting:

So the difference between 3% and 2% is 1%. The quotient, on the other hand, is calculated by dividing the two numbers. To avoid decimal numbers, the quotient is often given in percent:

So 3% is 150% of 2%. In order not to work with such large numbers, the relative difference is often used instead of the quotient. This is the quotient minus 100% or the difference relative to the starting value:

So 3% is a relative increase of 50% compared to 2%. Colloquially, this is often referred to as “a plus of 50%”. However, this expression can be misunderstood as a difference and is therefore better to avoid.

The term% does not make it clear which basis it is based on, i.e. whether the difference or the relative increase is meant. To distinguish one can therefore use the term “percentage points” for the difference. So the difference in this example would be 1 percentage point (one hundredth of the total) or 50% (fifty hundredth of the smaller portion). Mathematically, however, there is no difference between the two terms: a percentage point is equal to one percent is equal to 0.01 (one hundredth). The only difference is in the interpretation.

Unequal wholes

On closer inspection, it becomes clear that the term percentage point has different functions in the two examples. In example 1, two parts of the same total are considered. Both percentage values ​​and the percentage point refer to the same deposit. In this case, you can do without the term percentage points when speaking of an additional percent of the deposit.

The situation in the elections in example 2 is more difficult, since the same voters did not necessarily go to both elections. It is even conceivable that the proportion of 1% corresponds to more votes than the larger proportion of 2% if, for example, the turnout was significantly higher in the first election. In this case, the difference of one percentage point cannot be interpreted as a proportion of a total, but only as a purely mathematical difference.

Legal Regulations

In § 288 BGB it says: "The default interest rate for the year is five percentage points above the base rate ". With a base interest rate of 3%, the total default interest is 8%. In a lawsuit, interest on arrears should therefore also be applied for in the amount of 5 percentage points and not in the amount of 5% above the base rate. Otherwise, the plaintiff regularly demands significantly less than he is entitled to. Whether the court can award interest at the rate of 5 percentage points above the base rate on an application that formulates “percent” is controversial in the jurisprudence because of the procedural principle ne ultra petita , but is considered possible by the Federal Court of Justice by way of interpretation .

See also

Individual evidence

  1. For this OLG Hamm , judgment of April 5, 2005, Az. 21 U 149/04, full text = NJW 2005, 2238, 2239; on the other hand LAG Nürnberg , judgment of May 10, 2005, Az. 7 Sa 622/04, full text = NZA-RR 2005, 492, 495; OLG Koblenz , judgment of June 26, 2006, Az. 12 U 685/05, full text = NJW-RR 2007, 813, 815; LG Stralsund , decision of December 20, 2010, Az. 6 O 290/10, full text ; Doubtful also BAG , judgment of March 2, 2004, Az. 1 AZR 271/03, full text = NZA 2004, 852 ff.
  2. BGH , decision of February 7, 2013, Az.VII ZB 2/12, full text = NJW-RR 2013, 511.

Web links

Wiktionary: Percentage point  - explanations of meanings, word origins, synonyms, translations