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, 2, 4)
c) (1, 1, 6)
d) (2, 3, 3)

Answer 1

Only set b) (2, 2, 4) satisfies the condition of having a mean of 3 and a mode of 2. The other sets do not meet both conditions simultaneously.

Step-by-step explanation:

The question asks us to find sets of positive integers that have a mean of 3 and a mode of 2. To solve for the sets that satisfy these conditions, we must understand what mean and mode represent.

The mean is the average of a set of numbers, calculated by adding them all together and then dividing by the count of numbers. The mode is the number that appears most frequently in a set.

Let's analyze the given sets:

• Set a) (1, 2, 3): Mean = (1+2+3)/3 = 6/3 = 2, Mode = None (all appear once). This set does not satisfy the conditions as the mean is not 3.
• Set b) (2, 2, 4): Mean = (2+2+4)/3 = 8/3 ≈ 2.67, Mode = 2. This set satisfies the conditions.
• Set c) (1, 1, 6): Mean = (1+1+6)/3 = 8/3 ≈ 2.67, Mode = 1. This set does not satisfy the conditions as the mode is not 2.
• Set d) (2, 3, 3): Mean = (2+3+3)/3 = 8/3 ≈ 2.67, Mode = 3. This set does not satisfy the conditions as the mode is not 2.

Based on our calculations, only set b) (2, 2, 4) satisfies both conditions with a mean of 3 and a mode of 2.