Construct a set of ten numbers that have a mean of 8, median of 6 and a mode of 5.
Please help. Thank you!
To construct a set of ten numbers with a mean of 8, a median of 6, and a mode of 5, we will start by arranging the numbers in ascending order.
Since the median is 6, we know that the fifth and sixth numbers in the set will be 6.
Since the mode is 5, we want to include at least two occurrences of the number 5 in the set.
Now, let's break down the construction of the set step by step:
1. Start with two occurrences of the number 5: 5, 5.
2. To maintain a median of 6, we will add 6 and 6 as the fifth and sixth numbers in the set. The current set is: 5, 5, 6, 6.
3. Now, we need to determine the remaining six numbers to make the mean equal to 8. We want to distribute the numbers so that their sum is equal to (10 * 8) = 80, given that the current sum is 5 + 5 + 6 + 6 = 22.
Since we need to increase the sum by (80 - 22) = 58, we can add six instances of 9 to the set since 6 * 9 = 54.
4. Finally, add one instance of 10 to make the sum equal to 80.
Combining all the numbers, the set of ten numbers with a mean of 8, median of 6, and mode of 5 is:
5, 5, 6, 6, 9, 9, 9, 9, 9, 9.