1. **State the problem:** We are given a frequency distribution of the number of people at a public concert with values $X = 2, 3, 4, 5, 6$ and corresponding frequencies $T = 4, 2, 5, 3, 2$. We need to find the mean number of people. 2. **Formula for the mean of a frequency distribution:** $$\text{Mean} = \frac{\sum (X \times T)}{\sum T}$$ where $X$ is the value and $T$ is the frequency. 3. **Calculate the products $X \times T$ for each value:** - $2 \times 4 = 8$ - $3 \times 2 = 6$ - $4 \times 5 = 20$ - $5 \times 3 = 15$ - $6 \times 2 = 12$ 4. **Sum the products:** $$8 + 6 + 20 + 15 + 12 = 61$$ 5. **Sum the frequencies:** $$4 + 2 + 5 + 3 + 2 = 16$$ 6. **Calculate the mean:** $$\text{Mean} = \frac{61}{16} = 3.8125$$ **Final answer:** The mean number of people at the concert is $3.8125$.