Step 1: Write the fourteen yields against their serial position in a small table, since a quartile is just a marker on the ordered list of observations. Position: 1,2,3,4,5,6,7,8,9,10,11,12,13,14. Yield: 30,32,35,38,40,42,48,49,52,55,58,60,62,65.
Step 2: A quartile splits the ranked list into four equal parts, and the lower quartile Q1 sits one quarter of the way along the (n+1) spread of ranks, not simply at n/4. With 14 readings the spread of ranks runs from 1 to 15, so the target rank is $0.25 \times 15 = 3.75$.
Step 3: A rank of 3.75 falls three parts out of four between position 3 and position 4. Position 3 holds 35 kg/plot and position 4 holds 38 kg/plot, a gap of 3 kg/plot.
Step 4: Moving 0.75 of that 3 kg/plot gap forward from 35 gives the interpolated yield: $35 + 0.75 \times 3 = 35 + 2.25 = 37.25$ kg/plot.
Step 5: This figure, 37.25, is the only option consistent with correctly weighting between the two bracketing plots rather than rounding the rank up or down, so it is the 25th percentile.\[\boxed{Q_1 = 37.25\ \text{kg/plot}}\]