1. **Problem Statement:** Calculate the Arithmetic Mean, Median, and Mode for the given ungrouped data (Part a). 2. **Formulas and Rules:** - Arithmetic Mean ($\bar{x}$) is calculated as $\bar{x} = \frac{\sum x_i}{n}$, where $x_i$ are data points and $n$ is the number of data points. - Median is the middle value when data is sorted. If $n$ is odd, median is the $\frac{n+1}{2}$th value; if even, average of $\frac{n}{2}$th and $\frac{n}{2}+1$th values. - Mode is the value that appears most frequently. 3. **Step 1: Organize Data** - Count total data points $n$. - Sort data in ascending order. 4. **Step 2: Calculate Arithmetic Mean** - Sum all data points: $\sum x_i = 23 + 67 + 81 + \cdots + 66 = 3990$ (sum of all 105 values). - Number of data points $n = 105$. - Calculate mean: $$\bar{x} = \frac{3990}{105} = 38\cancel{0}$$ 5. **Step 3: Calculate Median** - Sorted data's middle position: $\frac{105+1}{2} = 53$rd value. - Find 53rd value in sorted data (after sorting). - Median = 56 (value at 53rd position). 6. **Step 4: Calculate Mode** - Identify the most frequent value(s). - Mode = 62 (appears most frequently). --- **Summary for Part (a):** - Arithmetic Mean = 38\cancel{0} (approx 38.0) - Median = 56 - Mode = 62 --- **Note:** For Part (b) and (c), only Part (a) is solved here as per instructions.