Question

Can you find sets of positive integers that satisfy the following?

Three numbers with mean 3 and mode 2
a. {1, 2, 3}
b. {2, 3, 4}
c. {1, 2, 2}
d. {1, 3, 4}

Answer 1

The set {2, 3, 4} satisfies the conditions of having a mean of 3 and a mode of 2.

Step-by-step explanation:

To find sets of positive integers that satisfy the given conditions, we are looking for three numbers whose mean is 3 and mode is 2.

Let's analyze the options:

a. {1, 2, 3} - The mean of this set is (1 + 2 + 3)/3 = 2. The mode is 2, but the mean is not 3.

b. {2, 3, 4} - The mean of this set is (2 + 3 + 4)/3 = 9/3 = 3. The mode is 2, and the mean is also 3, so this set satisfies the given conditions.

c. {1, 2, 2} - The mean of this set is (1 + 2 + 2)/3 = 5/3, which is not 3. The mode is 2, but the mean is not 3.

d. {1, 3, 4} - The mean of this set is (1 + 3 + 4)/3 = 8/3, which is not 3. The mode is 1, not 2.

Therefore, the only set that satisfies the given conditions is b. {2, 3, 4}.