1. **Problem:** Find the relationship between the mean, median, and mode of Alex's test scores: 60, 74, 82, 87, 87, 94. 2. **Calculate the mean:** $$\text{Mean} = \frac{60 + 74 + 82 + 87 + 87 + 94}{6} = \frac{484}{6} = 80.67$$ 3. **Find the median:** Sort scores: 60, 74, 82, 87, 87, 94 Median is the average of the 3rd and 4th scores: $$\text{Median} = \frac{82 + 87}{2} = \frac{169}{2} = 84.5$$ 4. **Find the mode:** The most frequent score is 87 (appears twice). 5. **Compare:** Mode = 87, Median = 84.5, Mean = 80.67 So, $$\text{Mean} < \text{Median} < \text{Mode}$$ **Answer:** D Mean < Median < Mode 2. **Problem:** Find the probability of spinning a number less than or equal to 2 or an even number from the bar graph data. 3. **Data:** Number: 1, 2, 3, 4, 5, 6 Times spun: 11, 4, 11, 9, 7, 5 Total spins = $$11 + 4 + 11 + 9 + 7 + 5 = 47$$ 4. **Event A:** Number less than or equal to 2 = numbers 1 and 2 $$P(A) = \frac{11 + 4}{47} = \frac{15}{47}$$ 5. **Event B:** Even numbers = 2, 4, 6 $$P(B) = \frac{4 + 9 + 5}{47} = \frac{18}{47}$$ 6. **Intersection (A \cap B):** Numbers less than or equal to 2 and even = number 2 $$P(A \cap B) = \frac{4}{47}$$ 7. **Use formula for union:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{15}{47} + \frac{18}{47} - \frac{4}{47} = \frac{29}{47}$$ **Answer:** B 15/47 + 18/47 - 4/47 3. **Problem:** 5 friends deposited an average of 2000 each. 3 deposited a total of 7500. The other 2 deposited equal amounts. Find how much one of the other 2 deposited. 4. **Total deposited:** $$5 \times 2000 = 10000$$ 5. **Amount deposited by other 2:** $$10000 - 7500 = 2500$$ 6. **Each of the other 2 deposited:** $$\frac{2500}{2} = 1250$$ **Answer:** B 1250 4. **Problem:** Find the probability of selecting a 2 from the list: 1 1 1 2 2 2 3 3 4 4 4 4 5. **Count total numbers:** 12 numbers total 6. **Count number of 2's:** 3 twos 7. **Probability:** $$P(2) = \frac{3}{12} = \frac{1}{4}$$ **Answer:** A 1/4