Given the data set: 12, 7, 4, 9, 0, 7, 3. a) Compute mean, median, and mode. b) Calculate Karl Pearson's coefficient of skewness and describe its shape.

Here is the solution for question 16. The given data set is 12, 7, 4, 9, 0, 7, 3. The sample size is n=7. First, sort the data in ascending order: 0, 3, 4, 7, 7, 9, 12. a) Compute mean, median, and mode of the data set. Step 1: Calculate the mean. The sum of the data points is x = 0 + 3 + 4 + 7 + 7 + 9 + 12 = 42. Mean (x) = ( x)/(n) = (42)/(7) = 6 Step 2: Calculate the median. The sorted data is 0, 3, 4, 7, 7, 9, 12. Since n=7 is an odd number, the median is the (n+1)/(2)-th value, which is the (7+1)/(2) = 4-th value. The 4th value in the sorted data is 7. Median = 7 Step 3: Calculate the mode. The mode is the value that appears most frequently in the data set. In the given data, the value 7 appears twice, which is more than any other value. Mode = 7 a) Mean = 6, Median = 7, Mode = 7 b) Calculate Karl Pearson's coefficient of skewness of the data set and also describe its shape. Step 1: Calculate the sample standard deviation (s). First, calculate the sum of squared differences from the mean: (x - x)^2. We found x = 6. (0-6)^2 = 36 (3-6)^2 = 9 (4-6)^2 = 4 (7-6)^2 = 1 (7-6)^2 = 1 (9-6)^2 = 9 (12-6)^2 = 36 The sum is $ (x - x)^2 = 36 + 9 + 4 + 1 + 1 + 9 +