To estimate the mean number of hours of sunshine, we first find the midpoints of each class interval:

• For \(30 \leq x < 60\), midpoint = 45
• For \(60 \leq x < 90\), midpoint = 75
• For \(90 \leq x < 110\), midpoint = 100
• For \(110 \leq x < 140\), midpoint = 125
• For \(140 \leq x < 180\), midpoint = 160
• For \(180 \leq x < 240\), midpoint = 210

Next, we calculate the weighted sum of the midpoints:

\(4 \times 45 + 8 \times 75 + 14 \times 100 + 25 \times 125 + 7 \times 160 + 2 \times 210 = 6845\)

The total number of years is 60. Therefore, the estimated mean is:

\(\text{Mean} = \frac{6845}{60} = 114.08\overline{3}\)