1. The problem involves analyzing the given data set: 30, 20, 40, 20, 30, 60, 80, 20, 40, 20. 2. First, let's state the problem clearly: We need to find measures of central tendency such as the mean and median, and possibly the mode, based on the data. 3. The formulas used are: - Mean: $$\text{Mean} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of data points. - Median: The middle value when data is ordered. - Mode: The most frequently occurring value. 4. Step-by-step calculations: - Order the data: 20, 20, 20, 20, 30, 30, 40, 40, 60, 80. - Calculate mean: $$\text{Mean} = \frac{30 + 20 + 40 + 20 + 30 + 60 + 80 + 20 + 40 + 20}{10} = \frac{360}{10} = 36$$ - Find median: Since $n=10$ (even), median is average of 5th and 6th values: 5th value = 30, 6th value = 30 $$\text{Median} = \frac{30 + 30}{2} = 30$$ - Find mode: 20 appears 4 times, 30 appears 2 times, 40 appears 2 times, others less. Mode is 20. 5. Explanation: - The mean gives the average value of the data. - The median gives the middle value, which is less affected by extreme values. - The mode shows the most common value in the data set. Final answers: - Mean = 36 - Median = 30 - Mode = 20