1. **Stating the problem:** We want to find the mean temperature from the histogram data with intervals and frequencies: - $4 \leq t < 6$ with frequency 6 - $6 \leq t < 8$ with frequency 10 - $8 \leq t < 12$ with frequency 4 2. **Formula for mean from grouped data:** $$\text{Mean} = \frac{\sum (f \times x)}{\sum f}$$ where $f$ is the frequency and $x$ is the midpoint of each interval. 3. **Calculate midpoints of each interval:** - For $4 \leq t < 6$: midpoint $= \frac{4 + 6}{2} = 5$ - For $6 \leq t < 8$: midpoint $= \frac{6 + 8}{2} = 7$ - For $8 \leq t < 12$: midpoint $= \frac{8 + 12}{2} = 10$ 4. **Calculate $f \times x$ for each interval:** - $6 \times 5 = 30$ - $10 \times 7 = 70$ - $4 \times 10 = 40$ 5. **Sum frequencies and weighted midpoints:** - $\sum f = 6 + 10 + 4 = 20$ - $\sum (f \times x) = 30 + 70 + 40 = 140$ 6. **Calculate the mean:** $$\text{Mean} = \frac{140}{20} = 7$$ **Final answer:** The mean temperature is $7$.