Argthtjtr

In data analyzed for the ‘Longman Grammar of Spoken and Written English’ on constructions with one in or one out of followed by a number, plural agreement predominated. ‘The Cambridge Grammar of English Usage’, which quotes this finding, comments that ‘For most writers the choice depends on whether you’re thinking of a single case or a general principle.’

"One in ten children" may be a fraction, but you are still talking about one child, even as a generality. Out of group of ten children at random, you are considering just one. The singular is/has is appropriate.

If you were to say "10% of children"or "a tenth of all children", then you are talking about a general group of children and the plural are/have is appropriate.

I think an alternative is:

One child in ten is dyslexic.

versus

One child in ten are dyslexic.

which seems to be incorrect. This puts the emphasis on the fact that there is one child, which is singular, that makes the verb be is rather than are.

I searched the New York Times's database for the phrase "one in ten" (note, the numbers are written as words), excluding modal and regular verbs used in the past tense that do not differentiate between singular and plural subjects, I did not find the phrase used with a plural verb until after 2010.

1. ONE IN TEN A PATIENT.; Dr. Briggs Tells Mental Trouble Increase in Massachusetts.
   
   BOSTON, Nov. 9.--One person in every twenty who dies in Massachusetts dies in a State institution, and one in every ten, at some time or another, enters an insane or feeble-minded hospital,… _{[November 10, 1921]}




2. FLORIDA REFUGEES NOW ARRIVING HERE
   
   “Every building in Fort Lauderdale is damaged,” Pope said, “and a hasty survey leads me to believe that not more than one in ten has been left standing. Only the most substantial houses stood up. Most houses are wrecks and many others have lost their roofs.
   _{[September 22, 1926]}




3. ONE IN TEN OF MANKIND IS NOW A RADIO LISTENER
   
   GENEVA. THE world's radio listeners now number 200,000,000, or one in ten of mankind, according to an estimate in Radiodiffusion, … _{[December 01, 1935]}




4. 1940 CENSUS FOUND ONE IN TEN JOBLESS; 5,110,000 Idle Out of Labor Force of 52,840,000 -- Women Gain Among 'New Workers'
   
   WASHINGTON, Jan. 5 -- One out of every ten workers of a total labor force of 52,840,000 in the United States was unemployed when the census was taken on March 30. About one out of every twenty of those working was reported to be employed by the Federal Government… _{[January 06, 1941]}




5. HEALTH PLAN HELD VAGUE TO DOCTORS; Ewing Says Not One in Ten Knows What President's Program Proposes
   
   WASHINGTON, Jan. 26—Oscar R. Ewing, Federal Security Administrator, said today President Truman's health insurance plan was basically different from the British system, which he recently studied at first-hand. _{[JAN. 27, 1950]}




6. One in Ten Shoppers Is a Shoplifter
   
   The team reported that one of every 10 of the shoppers walked out again with merchandise she did not pay for. (Overwhelmingly, shoplifters are she's.) _{[MARCH 15, 1970]}




7. How Will Europe Pay for Its Oil?
   
   Perhaps even more than the United States, the economy of Europe is powered by the automobile. One in ten jobs is dependent, directly or indirectly, on the health of this industry. Auto sales are off sharply–there was a slump of about 50 per cent in Germany in December–and manufacturers in one country… _{[January 20, 1974]}




8. Put More Teeth in Parole
   
   In theory, a prisoner released on parole is closely supervised and will be thrown back in prison if he violates the conditions of parole. But the public and many ex-cons regard supervision of parolees with cynicism. Parole officers' caseloads are heavy; supervision degenerates over time. Parolees perceive release as freedom, not as supervised release. One in ten absconds. _{[November 17, 1987]}




9. A LOWLY FISH GOES UPSCALE
   
   THE NEXT TIME YOU SIT DOWN TO A SEAFOOD dinner consider this: The chances are one in ten that what's in front of you was raised on a farm. According to the Fisheries Institute, aquaculture accounts for nearly all of the rainbow trout sold commercially in this country. _{[
   December 4, 1988]}

Examples, where a plural verb is (rarely) used.

10. Is Poverty a Kind of Robbery?
    
    …in 2011 low food security was a problem for just under one in eight whites — a matter of concern but for many white voters, a virtually invisible issue. Very low food security affects the lives of only one in 24 whites.
    
    For African Americans, low food security is a problem affecting one in four, and one in ten experience very low food security. _{[SEPTEMBER 16, 2012 11:57 PM]}




11. MacArthur Foundation Picks Eight Projects That Could Change the World
    
    “For the one in ten Americans who lack health insurance and need specialty care, the options are limited: pay out of pocket or delay treatment,” the foundation said.
    
    [FEB. 15, 2017]

I think it actually depends on the first number. If it is more than 1, then answers 1 and 4 should be used. If only one member of the set may fulfil the condition then 2 and 3.

User F.E. posted some relevant information in the comments to a question about a similar dilemma between two patterns of subject-verb agreement:

1. Only one out of three respondents (29%) thinks otherwise.


2. Only one out of three respondents (29%) think otherwise.

I wanted to reproduce these comments here to increase their visibility.

• 
  

  First of all, the subject isn't singular. The subject is a NP that has a plural head [...] both #1 and #2 versions are considered to be acceptable in today's standard English (according to the 2002 H&P's CGEL).
  – F.E. Jul 2 '15 at 18:12 




  
  



• 
  

  
  

  Basically the answer is this: Your sentence involves a proportional construction. Because the head ("respondents") of your subject is plural, that allows the plural verb ("think"); but due to the presence of "one", the optional singular override is also allowed which allows the singular verb ("thinks"). So, both plural and singular verbs are acceptable in your example sentence.

  
  

  
  
  

  – F.E. Jul 2 '15 at 19:59

  
  

This explanation seems to apply equally to
"One in ten children are dyslexic" vs. "One in ten children is dyslexic."

F.E. also left similar comments beneath the question "one in four kids": has or have? that have a few more details:

• 
  

  
  

  Both versions are acceptable and are standard English. For more info, there's the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL), page 504, in the section on proportional constructions, example [15.iii] "One in a hundred students takes/take drugs."

  
  

  
  
  

  – F.E. Feb 19 '15 at 20:49

  
  


• 
  

  
  

  Let me give you a brief explanation on your example. "Did you know [ (that) 1 in 4 kids has/have an undetected vision problem] ?" has a subordinate clause ("[ (that) 1 in 4 kids … problem]") and the subject of that subordinate clause is the noun phrase "one in four kids". The subject is plural in number due to the plural head "kids" and that supports a plural verb ("have"), but the singular "one" within the subject allows the optional singular override ("has").

  
  

  
  
  

  – F.E. Feb 19 '15 at 21:32