Question
8 (a) For a set of five numbers. the mode is 8 the median is 12 Work out one possible set of five numbers. [2 marks] __ __
Answer
3.4
(228 Votes)
Franklin
Professional · Tutor for 6 years
Answer
8, 8, 12, 13, 15This is one example of a possible set of five numbers satisfying the given conditions. Though the last two numbers, 13 and 15 in this solution, could be any two numbers larger than 12. The only condition needing to meet is they must be greater than 12 in both situations.
Explanation
## Step 1:Think about what mode and median mean in a set of numbers. The mode is the number that appears most often whilst the median is the middle number when the set is ordered from least to greatest. ## Step 2:Take the given mode to construct the first 2 numbers of our set where both numbers are equal to 8. This ensures that 8 repeats most often in the set.## Step 3:Now consider the median. The problem states the median is 12. Considering our list of numbers is supposed to be five in total, the median is in the third position. So, place 12 at our third position. Remember the numbers must be ordered from least to greatest. ## Step 4:Since we have to order this from least to greatest, we can’t go lower than 8, which appears to be the first two numbers. So the subsequent numbers after 12 have to be indeed larger than 12. We can choose any two numbers-taken at our will decidedly larger than 12.Remember, they can be any two numbers since no restrictions were given in the problem that restrain us in our choices and as there are no conclusions to be drawn charitably about those last two subsequent numbers. ## Important note:There could be many possible answers to this problem using the described approach.