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In this text, why do we use the past-perfect here instead of the simple past tense for "double"?

The chart shows the percentage of people aged 65 and over in the United States between 1900 and 2000. In the year 1900 just over 4% of the population was aged over 65. However, by 1960 this figure had doubled.

(emphasis added)

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    I'm not quite sure what you're asking. We use the past perfect tense there because that's exactly the situation in which you most commonly use past perfect. Can you edit to explain what part of that is confusing? – Nathan Tuggy May 16 '15 at 22:23
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    ... it had doubled... in 1960... who knows where it is now... it could have disappeared or quadrupled... – Catija May 16 '15 at 22:35
  • This is a hard question. It may be hard for native speakers to empathize with the confusion felt by a non-native speaker wondering why this sentence is in the past perfect. I see that you posted the question four years ago. Does the choice of past perfect tense seem less mysterious now? – Ben Kovitz Oct 18 '19 at 9:07
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I've suggested this reference when similar questions come up. Here's an excerpt explaining the two cases it is used:

  • The Past Perfect expresses the idea that something occurred before another action in the past. It can also show that something happened before a specific time in the past.

  • With Non-Continuous Verbs and some non-continuous uses of Mixed Verbs, we use the Past Perfect to show that something started in the past and continued up until another action in the past.

This is a bit tricky, but the way I'm understanding it, this sentence:

The chart shows the percentage of people aged 65 and over in the United States between 1900 and 2000.

establishes a context where we are talking about the population from 1900 to 2000.

So, the "before" action or specific time that this sentence references

However, by 1960 this figure had doubled.

is the percentage of people aged 65 and over in the United States in 2000 (the end of the implied progressive action of the population growing from 1900 to 2000).

The "before" action or specific time may not always be explicit. In cases like this where the connection is rather weak and the time is explicitly specified I don't believe it's wrong to just use the simple past tense.

However, by 1960 this figure doubled.

This doesn't sound wrong to me.

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