Subjects statistics and probability

Angle Median Probability 1C3E91

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1. **Stating the problem:** We are asked to find the angle $u$ in a circle diagram with given options 10°, 30°, 36°, and 45°. 2. **Understanding the problem:** The angle $u$ corresponds to a sector in a circle diagram. The size of the angle is proportional to the frequency or value represented by that sector. 3. **Formula used:** The angle of a sector in a circle diagram is given by $$\text{Angle} = \frac{\text{Value}}{\text{Total}} \times 360^\circ$$ 4. **Applying the formula:** From the bar chart, the values (antal skott) are 2, 3, 3, 2, 5, 2, and 3. The total number of skott is $$2 + 3 + 3 + 2 + 5 + 2 + 3 = 20$$ 5. If the sector marked $u$ corresponds to the value 2 (for example), then $$u = \frac{2}{20} \times 360^\circ = \frac{2}{20} \times 360 = 36^\circ$$ 6. **Answer:** The angle $u$ is $36^\circ$, which corresponds to option C. --- 1. **Stating the problem:** Find the median of the data from the bar chart. 2. **Data:** The values are 2, 3, 3, 2, 5, 2, and 3. 3. **Ordering the data:** Sort the data points: $$2, 2, 2, 3, 3, 3, 5$$ 4. **Median:** Since there are 7 data points, the median is the middle value, which is the 4th value: $$\text{Median} = 3$$ 5. **Answer:** The median is 3 points, option B. --- 1. **Stating the problem:** Given two consecutive rolls of five (two fives in a row), find the probability that the next roll is a five. 2. **Understanding the problem:** Each roll of a fair die is independent. 3. **Probability formula:** The probability of rolling a five on a fair six-sided die is $$P(5) = \frac{1}{6}$$ 4. **Answer:** The probability that the next roll is a five remains $\frac{1}{6}$, regardless of previous rolls. **Summary:** - Angle $u$ is $36^\circ$ (option C). - Median is 3 points (option B). - Probability of next roll being five is $\frac{1}{6}$.