1. Let's consider a problem involving mean (average): Find the mean of the data set $\{2, 4, 6, 8, 10\}$. To find the mean, sum all values and divide by the number of values: $$\text{Mean} = \frac{2+4+6+8+10}{5} = \frac{30}{5} = 6.$$ 2. A problem involving median: Find the median of $\{7, 3, 9, 5, 11\}$. First, arrange the data in ascending order: $\{3, 5, 7, 9, 11\}$. Median is the middle value, which is $7$. 3. A problem involving mode: Find the mode of $\{1, 2, 2, 3, 4, 4, 4, 5\}$. The mode is the value that appears most frequently, which is $4$. 4. A problem involving variance: Find the variance of $\{3, 7, 7, 19\}$. Step 1: Calculate mean: $$\mu = \frac{3+7+7+19}{4} = \frac{36}{4} = 9.$$ Step 2: Calculate squared deviations: $$(3-9)^2 = 36,\ (7-9)^2=4,\ (7-9)^2=4,\ (19-9)^2=100.$$ Step 3: Calculate variance: $$\sigma^2 = \frac{36+4+4+100}{4} = \frac{144}{4} = 36.$$ 5. A problem involving standard deviation: Using the variance above ($36$), standard deviation is the square root: $$\sigma = \sqrt{36} = 6.$$