Subjects statistics

Estimate Total Time 1Ca5Cf

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1. **State the problem:** We have a grouped frequency table showing time intervals and the number of runners in each interval. We want to estimate the total time of all runners combined. 2. **Formula and approach:** To estimate total time, multiply the midpoint of each interval by its frequency, then sum all these products. 3. **Calculate midpoints:** - For 0 < y \leq 5, midpoint = $\frac{0+5}{2} = 2.5$ - For 5 < y \leq 10, midpoint = $\frac{5+10}{2} = 7.5$ - For 10 < y \leq 15, midpoint = $\frac{10+15}{2} = 12.5$ - For 15 < y \leq 20, midpoint = $\frac{15+20}{2} = 17.5$ 4. **Multiply midpoints by frequencies:** - $2.5 \times 1 = 2.5$ - $7.5 \times 5 = 37.5$ - $12.5 \times 4 = 50$ - $17.5 \times 2 = 35$ 5. **Sum all products to estimate total time:** $$2.5 + 37.5 + 50 + 35 = 125$$ 6. **Answer:** The estimated total time of all runners is **125 seconds**.