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I'm wording a report on the averages of a discrete variable, and am trying to get the most appropriate sounding wording.

Consider the able below:

Average pets per household by income
Income ($) | Cats | Dogs
-----------+------+------
   < 20k   | 0.9  | 1.1
 20k - 50k | 1.5  | 2.0
   > 50k   | 2.0  | 1.9

Is it right to say:

The average number of dogs in low income households is 1.1.

While that's what the table states, its seems odd to talk about fractions of dogs. Contrast this with:

The average number of dogs in low income households was about 1.

This is right, but doesn't convey that it is above one, just near it. Lastly:

The average number of dogs in low income households was between 1 and 2.

This again seems odd as there isn't anything between 1 and 2.

Which of these is the most neutral and factual with respect to the data? Is there a better to way to word this accurately?

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    $\begingroup$ The average result from tossing an ordinary six-sided die (presuming it's sufficiently close to fair) is 3.5. Yes, you can't actually get that number from a single toss, but so? Averages don't have to have the property of being realizable in a single observation -- only as a population mean. Rounding to 1 dog may seem better somehow --- but it's perfectly possible nobody owns exactly 1 dog. If 39 people have no dog and one person has 44 dogs, "1 dog" is not inherently more or less meaningful than "1.1 dogs" (nobody has either quantity) ... but only one is the average. $\endgroup$
    – Glen_b
    Commented Feb 6, 2015 at 2:32
  • $\begingroup$ Out of curiosity, what would you propose to say was the average number of heads for a single coin toss? $\endgroup$
    – Glen_b
    Commented Feb 6, 2015 at 2:38
  • $\begingroup$ I wouldn't, I'd say there is a "one in two chance of a head". $\endgroup$
    – user40835
    Commented Feb 6, 2015 at 2:43
  • $\begingroup$ So for you the very concept of the mean disappears in that circumstance? [That suggests you may carry a very different idea of what an mean is than I think most statisticians do.] What if there were 50 people with 0 dogs and 50 with 1 dog? What's the average number of dogs? $\endgroup$
    – Glen_b
    Commented Feb 6, 2015 at 2:45
  • $\begingroup$ No, the mean still exists, I'm more focused on how to communicate it accurately to non-statistics educated people. In your example, I'm not as sure, which is why I'm seeking other opinions. $\endgroup$
    – user40835
    Commented Feb 6, 2015 at 2:47

2 Answers 2

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The number of dogs in a household is a count. It is true that you cannot have $1.1$ dogs, but it is also true that the average of the number of dogs in low income households can well be $1.1$. There is nothing necessarily incorrect about this claim, and your top phrasing is the right one to use.

What people sometimes say (which sounds the same, but is incorrect), is: 'the average low income household has $1.1$ dogs'. It isn't clear what an 'average low income household' is, and it certainly can't have $1.1$ dogs. As you haven't made that error, you have nothing to worry about.

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If you really thought your readers/listeners would struggle to make sense of a non-integer number of dogs you could perhaps say

On average, ten low-income households will own eleven dogs between them.

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