1. **Problem Statement:** Calculate the mean, median, and mode of the data set: 34, 33, 32, 31, 40, 39, 45, 32, 30, 32. 2. **Mean:** The mean is the average of all numbers. Formula: $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. Calculate the sum: $$34 + 33 + 32 + 31 + 40 + 39 + 45 + 32 + 30 + 32 = 348$$ 4. Number of data points: 10 5. Calculate mean: $$\frac{348}{10} = 34.8$$ 6. **Median:** The median is the middle value when data is ordered. Steps: - Order data: 30, 31, 32, 32, 32, 33, 34, 39, 40, 45 - Since there are 10 (even) data points, median is average of 5th and 6th values. - 5th value = 32, 6th value = 33 - Median: $$\frac{32 + 33}{2} = 32.5$$ 7. **Mode:** The mode is the most frequent value. - Values and frequencies: 32 appears 3 times, others less. - Mode = 32 **Final answers:** - Mean = 34.8 - Median = 32.5 - Mode = 32