Give two examples of data that satisfy each of the following conditions: (i) 3 numbers whose mean is 8. (ii) 4 numbers whose median is 15.5. (iii) 5 numbers whose mean is 13.6. (iv) 6 numbers whose mean = median. (v) 6 numbers whose mean > median.
Example 1: 6, 8, 10 (sum = 24, mean = 24/3 = 8). Example 2: 7, 8, 9 (sum = 24, mean = 8).
Example 1: 10, 14, 17, 20 (sorted: 10, 14, 17, 20, median = (14+17)/2 = 15.5). Example 2: 12, 15, 16, 18 (median = (15+16)/2 = 15.5).
Example 1: 10, 12, 14, 16, 16 (sum = 68, mean = 68/5 = 13.6). Example 2: 11, 13, 13, 14, 17 (sum = 68, mean = 13.6).
Example 1: 1, 2, 3, 4, 5, 6 (mean = 3.5, median = (3+4)/2 = 3.5). Example 2: 2, 4, 6, 8, 10, 12 (mean = 7, median = 7).
Example 1: 1, 2, 3, 4, 5, 20 (mean = 35/6 5.83, median = 3.5). Example 2: 1, 1, 2, 3, 4, 15 (mean = 26/6 4.33, median = 2.5).
Explanation
(i) Three numbers summing to 24 will have mean 8. (ii) For 4 numbers, median is the average of the 2nd and 3rd values when sorted. (iii) Five numbers summing to 68 will have mean 13.6. (iv) Symmetric distributions have equal mean and median. (v) Data with high outliers (right-skewed) has mean greater than median.