What is the normal range of variation for tsh between blood tests taken throughout the year for a person not on any meds?

Normal is normal: Normal runs 0.5-4.5miu/ml approximately. Some argue that normals should be adjusted to 0.4-2.5 miu/ml. Everyone varies a little and there is always laboratory variation. As long as you are not clearly trending and don't have high levels of associated thryoid antibodies i wouldn't worry about what is probably normal variation.

<10%: Tsh is secreted by the pituitary gland as a stimulator of thyroid hormone production. Depending on your thyroid gland function, the TSH value will be reciprocally elevated or decreased. It is a servo mechanism: TSH does down when T4 or T3 (liothyronine) is up. It is a constant fine tuning. But, in general, it does not alter more than 10% during a year.