Final answer:
To find the possible sets of five positive integers with a range, mode, median, and mean equal to 10, we need to analyze the properties of these statistics.
Step-by-step explanation:
To find the possible sets of five positive integers with a range, mode, median, and mean equal to 10, we need to analyze the properties of these statistics. Let's start by considering the range. Since the range is equal to 10, the minimum and maximum values in the set must have a difference of 10. One possible set that satisfies this condition is:
1, 2, 3, 12, 13
Now, let's look at the mode. The mode is the value that appears most frequently in a set. In this case, the mode is 10 since it appears three times. To maintain a mode of 10, we can adjust our previous set:
1, 2, 10, 10, 11
Next, let's consider the median. The median is the middle value when the set is arranged in numerical order. To maintain a median of 10, we can modify our set:
4, 7, 10, 10, 13
Finally, let's calculate the mean. The mean is the average of all the values in a set. The sum of the set must be equal to 5 multiplied by the mean. Since the mean is 10, the sum of the set must be 50. Here's a possible set that satisfies this condition:
5, 9, 10, 12, 14
Therefore, one possible set of five positive integers with a range, mode, median, and mean equal to 10 is 5, 9, 10, 12, 14.