An agricultural student plans to estimate the average soil nitrate concentration (in $mg/kg$) across a large farm to assess its overall nutrient profile. The farm contains three distinct management zones: a heavily fertilized arable field, a sheep-grazed pasture, and a naturally low-nutrient wildflower meadow.

The student's plan is as follows:

• Use a random number generator to generate $10$ coordinates across a digital map of the entire farm.
• Collect a single $50g$ soil core sample from each of these $10$ coordinates.
• Use a basic home-testing colorimetric kit (which classifies nitrate levels into four broad categorical bands: Low, Medium, High, and Very High) to record the nitrate level of each sample.