# Ambivalence about the 'respective' rate of increase (or decrease?) in the statements of type

Here is a sentence:

"In the United States between 1850 and 1880, the number of farmers continued to increase, but at a rate lower than that of the general population."

Now, from this, I infer that the rate of increase in the number of farmers during the 30 years was not at par or higher than the rate at which the whole population increased.

Eg. The population may have increased by 3% but the no. of farmers increased by 1%. Correct?

As an hypothetical example, if the population was 100 persons with 10 farmers, now it is 103 with 1 farmer (total 11). Right?

My doubt is, The place where I read this text had a related question asking what contradicts the statement.. and the answer read:

"The proportion of farmers in the general population increased from 68 percent in 1850 to 72 percent in 1880."!

EDIT >>

For the reason that members are not interpreting the question as it deems to be, here's some additional info:

First of, note that the doubt is NOT related to the 'math' or values involved in the example. The doubt is about the fact that where I read the original statement, had an accompanied question asking that which of the statements 'contradict' the original statement.

Hence, the doubt that I had is that how the second statement that mentions that there 'was' an increase in the proportion of farmers, contradict the original statement.

Hope I make my point clear now and yes, this question IS related to ENGLISH and not MATHS.

Any further doubts, kindly consider clarifying in the comments.

• There is something wrong with that latter sentence. The proportion of farmers in America would quite definitely not have been 72% in 1872. In Britain, on the eve of the First World War (1914) the country only had 9% of the workforce in agriculture. It was by far the lowest in Europe, but even Germany and France was only about 30%. And that refers to all agricultural workers, not just 'farmers'. – WS2 Feb 20 '15 at 15:40
• The question asked for something that contradicts the initial sentence, and the last statement definitely does contradict it, so what's the confusion? – Hellion Feb 20 '15 at 15:59
• In your hypothetical example, the rate of increase among farmers is 10%, not 1%. – JeffSahol Feb 20 '15 at 16:02
• The cited text is inherently ambiguous, since it all depends on exactly what rate means in the specific context. Suppose there were 10M Americans in 1850, and the number of farmers increased at the rate of 1M per year, whereas the general population only increased at the rate of 1.1M per year? That could be a true statement, since 1M is definitely lower than 1.1M. Admittedly it would need to be in some alternate universe with a slightly different history but the same language, but rate of increase doesn't automatically imply as a percentage [of the previous value]. – FumbleFingers Feb 20 '15 at 18:22
• I'm voting to close this question as off-topic because it is based on an error in math, not a problem of English. – Hellion Feb 21 '15 at 15:14

## 1 Answer

Let's modify your "sample" numbers just slightly:

• initial population = 1000
• farmers = 100
• therefore, proportion of farmers to population = 100/1000 = 10%

Now, as specified, the number of farmers grew, but slower than the general population did:

• final population grew by 3%: 1030
• farmers grew by 1%: 101
• proportion of farmers to population = 101/1030 = 9.803%

If the farmer's population grows at a slower rate than that of the general populace, it is a simple mathematical relationship that their percentage of the total populace cannot increase. This is more of a math problem than an English problem, as your question's initial example had the farmers increasing by 10%, which was more than the overall population growth rate, which was probably throwing off your calculation.

• "If the farmer's population grows at a slower rate than that of the general populace, it is a simple mathematical relationship that their percentage of the total populace cannot increase. " Oh! I see. So that is the point that makes the second statement contradict the original. Yes, I agree that it is now clear by the example you quoted Hellion. Well, now it does seem more related to the mathematical interpretation than english. Nevertheless, thank you for clearing the doubt. It helps! – Vaibhav Feb 23 '15 at 7:03