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The sentence below is a rewrite by a native speaker of the text in the red box. I have a feeling that changing "families" to "a family" is correct. I think it means something like an average family. I would like to know exactly why "a family" works.

The bar graph presents data on how a family, located in one particular country, spent their weekly income in 1968 and 2018.

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You'll see that the figures are averages. This means that the results were calculated using the spending of many families. Replacing 'families' with 'a family' would therefore be incorrect.

You could perhaps replace it with the average family, although this would not be consistent with the way that the results were then presented.

For example, you could say either:

  • The average family spent 20% of their income on food.
  • Families spent an average of 20% of their income on food.

So, you can present precise values as the spending for 'the average family', but if you are presenting the values themselves as averages, you must refer to the entire cohort from which they were calculated.

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  • Sorry, I don't understand your explanation after the two example sentences you gave. Do these two sentences mean the same? 1. The average family spent 20% of their income on food. 2. Families spent an average of 20% of their income on food.
    – Learner110
    Jul 22 at 13:33
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    @Learner110 What I mean is that it would sound wrong to say "the average family spent an average....". Not just because you're repeating the word 'average', but because it makes no mathematical sense. You have to express it one way or the other. Your sentence is leading into a presentation of average numbers, so it would be wrong to say these belong to 'the average family'.
    – Astralbee
    Jul 24 at 8:40

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