In a set of five one-digit numbers where the mode is three and the median is six, what is the smallest number if the mean is 5.4?

To solve the problem, we need to analyze the given conditions about the set of five one-digit numbers.

1. Mode is 3: This means that the number 3 appears more frequently in the set than any other number. Since there are only five numbers and the mode is 3, at least two of the numbers must be 3.

2. Median is 6: For a set of five numbers, the median will be the third number when the numbers are arranged in order. Therefore, the sequence must be such that the middle number (when the numbers are sorted) is 6.

3. Mean is 5.4: The mean is calculated by dividing the sum of the numbers by the number of elements. In this case, since there are five numbers, the total sum must be ( 5.4 \times 5 = 27 ).

With these constraints in mind, let's construct the set:

• We need two of the numbers to be 3 (to satisfy the mode), and the third number must be 6 (to satisfy the median). So, we can start forming the set as (3, 3, 6, x, y),