1. **Problem:** Compute the population mean, median, and mode for the first ungrouped data set given. 2. **Formula and rules:** - Mean: $\bar{x} = \frac{\sum x_i}{n}$ where $x_i$ are data points and $n$ is the number of data points. - Median: The middle value when data is ordered. If $n$ is odd, median is the middle value; if even, average of two middle values. - Mode: The value that appears most frequently. 3. **Data:** Population (x) = [12, 56, 34, 7, 32, 45, 15, 38, 23] 4. **Calculate Mean:** $$\sum x = 12 + 56 + 34 + 7 + 32 + 45 + 15 + 38 + 23 = 262$$ Number of data points $n = 9$ $$\text{Mean} = \frac{262}{9} \approx 29.11$$ 5. **Calculate Median:** Sort data: [7, 12, 15, 23, 32, 34, 38, 45, 56] Middle value (5th) is 32 $$\text{Median} = 32$$ 6. **Calculate Mode:** All values appear once, so no mode or all values are modes. Here, no repeated value, so no mode. **Final answers:** - Mean $\approx 29.11$ - Median $= 32$ - Mode $= \text{None}$ "slug": "population stats", "subject": "statistics", "desmos": {"latex": "y=0", "features": {"intercepts": true, "extrema": true}}, "q_count": 4