Following a Freedom of Information request submitted by the Howard League for Penal Reform, North Yorkshire Police released figures showing there had been a significant rise in the number of children aged 17 and under arrested by officers in 2011.
However, further analysis of the data has indicated that the force gave a figure that was significantly higher than it should have been.
The discrepancy was the result of a mistake made during counting by a member of staff.
The actual arrest figures for people aged under 18 over the last four years are:
Temporary Chief Constable Tim Madgwick, of North Yorkshire Police, said:
"The mathematical error in gathering the data to answer the Freedom of Information request from the Howard League for Penal Reform is very disappointing and regrettable.
"On behalf of North Yorkshire Police, I sincerely apologise to the Howard League and other parties that have been inconvenienced by this error.
"I will send a letter of apology to the Howard League as a matter of priority."
Mr Madgwick added: "Following a review of the data, I can confirm the correct number of juveniles arrested by North Yorkshire Police in 2011 was 2,953.
"This is in line with the year-on-year national trend of decreasing numbers of under 18s who are placed under arrest."
North Yorkshire Police follows national guidance when dealing with juveniles linked to crime and anti-social behaviour.
Mr Madgwick said: "If it is necessary to arrest a juvenile who is suspected of committing an offence, we make every effort to achieve the most positive outcome for both the victim and offender.
"This approach includes actively engaging with the young person and their family and working with partners within the criminal justice system and other agencies.
"The aim is to divert them away from a life of crime and the misery that goes with it, and become responsible members of society."
5.48pm - 3 December 2012