1. **State the problem:** We have data for years (x) and stamp costs in cents (y). We need to analyze the data by plotting, summarizing, and finding equations for lines related to the data. 2. **Data given:** Years (x): 1975, 1978, 1981, 1985, 1988, 1991, 1995, 1999, 2001, 2006, 2011 Costs (y): 13, 15, 18, 22, 25, 29, 32, 33, 34, 39, 44 3. **Find the five-number summary for x and y:** - Sort x (already sorted): 1975, 1978, 1981, 1985, 1988, 1991, 1995, 1999, 2001, 2006, 2011 - Minimum x = 1975 - Maximum x = 2011 - Median x (middle value) = 1991 (6th value) - Lower quartile Q1 x = median of lower half (1975, 1978, 1981, 1985, 1988) = 1981 (3rd value) - Upper quartile Q3 x = median of upper half (1995, 1999, 2001, 2006, 2011) = 2001 (3rd value) - Sort y (already sorted): 13, 15, 18, 22, 25, 29, 32, 33, 34, 39, 44 - Minimum y = 13 - Maximum y = 44 - Median y = 29 (6th value) - Lower quartile Q1 y = median of lower half (13, 15, 18, 22, 25) = 18 (3rd value) - Upper quartile Q3 y = median of upper half (32, 33, 34, 39, 44) = 34 (3rd value) 4. **Write the quartile points (Q-points):** - Q1 point: (1981, 18) - Q3 point: (2001, 34) 5. **Find the equation of the line through Q-points:** - Slope $m = \frac{34 - 18}{2001 - 1981} = \frac{16}{20} = 0.8$ - Use point-slope form with Q1 point: $$y - 18 = 0.8(x - 1981)$$ - Simplify to slope-intercept form: $$y = 0.8x - 0.8 \times 1981 + 18 = 0.8x - 1584.8 + 18 = 0.8x - 1566.8$$ - Rounded to nearest tenth: $$y = 0.8x - 1566.8$$ 6. **Interpretation:** This line models the cost of stamps over years based on the quartile points. "slug":"stamp cost analysis","subject":"statistics","desmos":{"latex":"y=0.8x-1566.8","features":{"intercepts":true,"extrema":true}},"q_count":5