# Is percentage similar to proportion ?

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#### duiter

##### Member
Dear all,

1. Is percentage similar to propertion in terms of meaning ?
Is it interchangable ?

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2. Is the word 'term' in 'in terms'always in plural form ('terms') ?

Is it wrong to say 'in term' ( without 's' at the end of the word 'term' ) ?

Thanks

#### corum

##### Senior Member
Dear all,

1. Is percentage similar to propertion in terms of meaning ?
Is it interchangable ?

Suppose the proportion of men to women in a class is 1:4 (the number if people does not matter now). In other words, 4:1 equals to the proportion of women to men.
It means if you randomly divide the people in the class into groups of five and you pick out a single group, the most likely distribution of sexes would be one male individual against four female individuals.

Now let me express the situation in terms of percentage. You will have to draw your conclusions.

Suppose the percentage of men in a class of mixed sexes is 20%. In other words, women comprise 80% of the class. Now, if you randomly divide the class into groups of five, it won't on average affect the percentage. Right? This means if I pick out a single group of five people, the most likely distribution of sexes would be one he and four she. Same as with the proportional example. Why?

80% = 4*(20%)
20% = 1*(20%)

4:1 appears here too.

Is it wrong to say 'in term' ( without 's' at the end of the word 'term' ) ?

Yes, it is.

#### bertietheblue

##### Senior Member
Suppose the proportion of men to women in a class is 1:4 (the number if people does not matter now). In other words, 4:1 equals to the proportion of women to men.
It means if you randomly divide the people in the class into groups of five and you pick out a single group, the most likely distribution of sexes would be one male individual against four female individuals.

Now let me express the situation in terms of percentage. You will have to draw your conclusions.

Suppose the percentage of men in a class of mixed sexes is 20%. In other words, women comprise 80% of the class. Now, if you randomly divide the class into groups of five, it won't on average affect the percentage. Right? This means if I pick out a single group of five people, the most likely distribution of sexes would be one he and four she. Same as with the proportional example. Why?

80% = 4*(20%)
20% = 1*(20%)

4:1 appears here too.

Yes, it is.

This isn't quite the full picture. I've written a more detailed comparison below. (None of what follows has been researched; it is based solely on my observations so corrections, additions and clarifications from other people are welcome.)

1. Sometimes 'proportion', whilst not interchangeable with 'percentage', means the same thing, where:

proportion means a given amount of a total amount, whether that amount is a percentage or a number - it has more of a general meaning than 'percentage'

percentage means a given percentage of a total percentage (ie 100%)

Consider:

(a) 'The number [possibly 'proportion' although 'number' is more usual] of women in the Houses of Parliament has risen following the election from x to y' (where the total number of Members of Parliament (MPs) is 650) - note that with 'number' we are simply stating the number; with 'proportion' we are giving the number as a share of the total amount, so what we are actually saying here is 'The proportion of women has risen ... from x to y out of 650', but if the total amount is not understood by the audience then we would use 'number'.

(b) 'The percentage [or 'proportion', or even 'number' - 'The number of doctors in the UK has risen by 15% since 2000')] of women in the Houses of Parliament has risen following the election from a% to b%' (where 100% = 650)

I would be more likely to use 'proportion' if I didn't give figures:

'The proportion of women in the Houses of Parliament has risen following the election.'

since both 'number' and 'percentage' raise the questions of 'what number?', 'what percentage?'.

Whether to use percentage/proportion or number/proportion would simply depend on the purpose of the relevant statistic. Percentages have the advantage of being universally understood. For example, if you wanted to compare the numbers of women in government by country, you would use percentages since only the UK has 650 MPs so it'd be useless talking about the actual number of female MPs.

Note if the amount we talk about is considerably less than 1%, we tend to abandon percentages - 'per [factors of 10 over 100, eg 1,000, 100,000, 1 million]' is common more:

'The murder rate in the UK is 12.5 per 100,000' (as a percentage: 0.0125% - besides, we don't usually imagine people as percentages)

You will note in the above sentence the use of 'rate'. This is often used for statistics about the population as a whole, where the percentage is small: the 'murder rate', 'heart attack rate', 'abortion rate', 'crime rate', 'suicide rate', 'fertility rate'. If not qualified by 'per 1,000', etc 'rate' means percentage. It is used in particular in certain economic terms: 'interest rate' ('lending rate', 'borrowing rate'), 'growth rate', 'rate of inflation'/'inflation rate', 'deficit rate', but 'debt as a percentage of gross domestic product [or more usually, GDP]'

Other examples of 'per':

'The number of doctors in the UK is 8.8 per 1,000 people.'

Common in science for minute percentages is 'parts per million (ppm)':

'Carbon dioxide in the Earth's atmosphere is at a concentration of 391 ppm by volume.'

(i) When talking about change we usually use percentages:

'The crime rate has fallen by 2% in the last year.'

'The number of doctors has risen by 15% since 2000.'

(ii) As can be seen from some of the examples above, the % symbol is enough to tell us we are talking about percentages and often we use a different word in the subject - we might write, as appropriate, 'the rate/proportion/number is x%'

Oh, and which is right: 'percent'/'per cent.'/'per cent'/'%'? Answer: all*, although I'd stick with '%' in almost all cases

* When I started working at my company the house style (except in tables where it's always been '%') was 'per cent.'. It then changed to 'per cent' and now finally the powers that be have sensibly gone with '%'.

2. 'proportion' is more or less interchangeable with 'ratio': both mean a share of one thing relative to the share of another thing, both of which are contained within a whole.

The proportion of x [relative] to y is [3 to 2][3 : 2].
'The ratio of x [relative] to y is 3 : 2.'/'The x to y ratio is 3 : 2.'

As with 'percentage', you will see 'ratio' more often than 'proportion' in scientific/mathematical texts.

Little known fact: a space either side of the colon is the convention in science; no space is more common in general use.

And there, I run out of steam! Please feel free to add.

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