Jo Farrell endorsed the statement of her predecessor, Sir Iain Livingstone, that the single force had a racism problem. Before his retirement in May he said that Police Scotland “is institutionally racist and discriminatory”.

Sir Iain told a meeting of the Scottish Police Authority: “It is right for me, as chief constable, to clearly state that institutional racism, sexism, misogyny and discrimination exist. Publicly acknowledging these issues exist institutionally is essential to our absolute commitment to championing equality and becoming an anti-racist service.”

Ms Farrell said in a statement: “Having considered Sir Iain’s reasons, I agree Police Scotland is institutionally discriminatory.

“People with different backgrounds or experiences, including our officers and staff, have not always received the service that is their right. The onus is on us to challenge bad behaviour and prejudice, address gaps and eradicate bias, known or unwitting, at every level.”

The force’s Policing Together scheme is designed to address this.

At her swearing-in ceremony at Police Scotland headquarters at Tulliallan, Ms Farrell said: “My operational focus is on threat, harm and risk. Police Scotland will focus on prevention, problem-solving and proactivity, and on looking after our hard-working officers and staff so our people can deliver our vital public service.

“Police Scotland is a highly credible public sector organisation known for its compassion and it attracts huge public support. It is a privilege to be entrusted with the leadership of so many talented, professional and courageous police officers, staff and volunteers.”

The Scottish Police Federation, the body for rank-and-file officers, said: “The new chief constable has to prioritise resourcing and police numbers as the current operating model is unsustainable for police officers’ welfare and for the communities they serve. There are not enough officers to answer the calls, never mind enough of them to attend the calls.

“The chief constable must publicly challenge the government and force a U-turn in the financial policies that are threatening public safety and the detection of crime.”