Question

For a set of five whole numbers, the mean is 4, the mode is 1, & the median is 5. What are the five numbers?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the five numbers, let's start with the mode being 1. Since the mode is the number that appears the most frequently, we know that one of the numbers is 1.

Now let's consider the median being 5. The median is the middle number when the numbers are arranged in ascending order. So, we know that one of the numbers is 5.

Since the given numbers are whole numbers and the mean is 4, the sum of all five numbers is 5 × 4 = 20.

Now we can consider the remaining numbers. To satisfy the mean of 4 and have a sum of 20, the remaining three numbers must have a sum of 20 - 1 (mode) - 5 (median) = 14.

Let's list down possible combinations for the remaining three numbers (keeping in mind they are distinct whole numbers and sum to 14):
- 2, 4, 8
- 2, 5, 7
- 3, 4, 7
- 3, 5, 6

To check which combination fulfills the conditions, we can calculate their mean:
- For 2, 4, 8: (1 + 5 + 2 + 4 + 8) / 5 = 20 / 5 = 4 (mean is correct)
- For 2, 5, 7: (1 + 5 + 2 + 5 + 7) / 5 = 20 / 5 = 4 (mean is correct)
- For 3, 4, 7: (1 + 5 + 3 + 4 + 7) / 5 = 20 / 5 = 4 (mean is correct)
- For 3, 5, 6: (1 + 5 + 3 + 5 + 6) / 5 = 20 / 5 = 4 (mean is correct)

All combinations fulfill the mean condition, so now let's see which combinations have the median of 5:
- For 2, 4, 8: The numbers are 1, 2, 4, 5, 8 (median is incorrect)
- For 2, 5, 7: The numbers are 1, 2, 5, 5, 7 (median is correct)
- For 3, 4, 7: The numbers are 1, 3, 4, 5, 7 (median is correct)
- For 3, 5, 6: The numbers are 1, 3, 5, 5, 6 (median is correct)

Hence, the set of five whole numbers that satisfy the given conditions is either {1, 2, 5, 5, 7} or {1, 3, 4, 5, 7}.

Answer 2

sorry -- the median of {1, 3, 4, 5, 7 is 4.

and the mode of {1, 2, 5, 5, 7} is 1
so neither of your answers is correct.

so let's start with the median and mode: {1,1,5,x,y}
The mean is 4, so the sum is 20.
That gives us {1,1,5,6,7}

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. You are correct.

The set of five whole numbers that satisfy the given conditions is {1, 1, 5, 6, 7}.