Subjects statistics

Frequency Density 620E0C

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1. **Stating the problem:** We are given a histogram showing frequency density of sharks at different depth intervals. We want to find the frequency (number of sharks) between depths 72 m and 100 m. 2. **Understanding frequency density:** Frequency density is defined as frequency divided by class width: $$\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$$ 3. **Formula to find frequency:** Rearranging the formula: $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$ 4. **Identify intervals and frequency densities between 72 m and 100 m:** - From 70 m to 80 m: frequency density is about 1.5 - From 80 m to 100 m: frequency density is about 0.3 5. **Calculate frequencies for each interval:** - Interval 70 to 80 m: Class width = $80 - 70 = 10$ m Frequency = $1.5 \times 10 = 15$ - Interval 80 to 100 m: Class width = $100 - 80 = 20$ m Frequency = $0.3 \times 20 = 6$ 6. **Calculate total frequency between 72 m and 100 m:** Since 72 m is within the 70-80 m interval, we calculate the partial frequency for 72 to 80 m: - Partial class width = $80 - 72 = 8$ m - Partial frequency = $1.5 \times 8 = 12$ Add the full frequency for 80 to 100 m: - Total frequency = $12 + 6 = 18$ **Final answer:** The estimated number of sharks between depths 72 m and 100 m is **18**.