Statisticians involves a lot of work where you could be in contact with the public which increases your needs for a public liability insurance policy. While it is not legally required to have a public liability policy it is advised to cover yourself against any liability claims for instance injury to the public caused by your negligence. The cost of a public liability insurance policy for a statistician is negligible when you compared the cost with the risk of a defending yourself against a public liability claim without any insurance. Liability claims are often for thousands and even millions of pounds which is obviously enough to bankrupt most businesses if they don’t have an insurance policy to cover themselves.
If you have even one employee then you must (by law) have an employers liability insurance policy in place, not having a policy in place if required is not only illegal but irresponsible since you are leaving your business open to large liability claims which could ultimately mean the end of your business. An employers liability insurance policy would usually cover you if an employee was to hold you liable for any injury they sustained while working under the direction of you. As you can imagine these claims for injury will often be for very large amounts of money.