Final answer:
To find the numbers in the set of data given the mean, median, and mode, we start by arranging the numbers in ascending order. The mode is 4 and occurs 3 times, so we can fill in the missing numbers with 4. Then, by calculating the sum of all the numbers and subtracting it from the sum of the given numbers, we find the missing number. The numbers in the set of data are 4, 4, 4, 4, 4, 4, and 7.
Step-by-step explanation:
To find the numbers in the set of data, we need to consider the given information:
- Mean = 7
- Median = 7
- Mode = 4 and occurs 3 times
Since the mean and median are the same, it means that the data is symmetrically distributed. We can start by arranging the numbers in ascending order:
4, 4, 4, __, __, __, 7
The mode is 4 and occurs 3 times, so we can fill in the missing numbers with 4:
4, 4, 4, 4, 4, 4, 7
Now, to find the remaining number, we can calculate the sum of all the numbers and subtract it from the sum of the numbers we have:
Sum of all numbers = (4 × 3) + 7 = 19
Sum of given numbers = (4 × 6) + 7 = 31
Missing number = Sum of all numbers - Sum of given numbers = 19 - 31 = -12
Therefore, the numbers in the set of data are: 4, 4, 4, 4, 4, 4, and 7.