1. **State the problem:** We are given the dataset $\{51, 39, 43, 46, 53, 63, 35, 57, 61, 22\}$ and need to calculate the mean, median, and mode. 2. **Mean formula:** The mean (average) is calculated by summing all values and dividing by the number of values: $$\text{Mean} = \frac{\sum x_i}{n}$$ where $x_i$ are the data points and $n$ is the number of data points. 3. **Calculate the mean:** Sum the numbers: $$51 + 39 + 43 + 46 + 53 + 63 + 35 + 57 + 61 + 22 = 470$$ Number of data points $n = 10$ Calculate mean: $$\text{Mean} = \frac{470}{10} = 47$$ 4. **Median formula:** The median is the middle value when the data is sorted. If $n$ is even, median is the average of the two middle numbers. 5. **Calculate the median:** Sort the data: $$22, 35, 39, 43, 46, 51, 53, 57, 61, 63$$ Since $n=10$ (even), median is average of 5th and 6th values: $$\text{Median} = \frac{46 + 51}{2} = \frac{97}{2} = 48.5$$ 6. **Mode:** The mode is the value that appears most frequently. Here, all numbers appear once, so there is no mode. **Final answers:** - Mean = 47 - Median = 48.5 - Mode = None (no repeated values)