Question

The mean of number 2, 4, 6, 8 is ____.

• A. 4
• B. 5
• C. 6
• D. 8

Hint:

For a set of numbers in a perfect arithmetic progression (like 2, 4, 6, 8), the mean is always exactly in the middle of the two center terms. The middle of 4 and 6 is 5.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The arithmetic mean (or average) is a measure of central tendency calculated by dividing the sum of all values in a data set by the total number of values.

Step 2: Key Formula or Approach:
\[ \text{Mean} (\bar{x}) = \frac{\sum x_i}{n} \] where \( \sum x_i \) is the sum of observations and \( n \) is the number of observations.

Step 3: Detailed Explanation:
1. Sum of the numbers: \( 2 + 4 + 6 + 8 = 20 \). 2. Total count of numbers (\( n \)): 4. 3. Calculation: \[ \text{Mean} = \frac{20}{4} = 5 \]

Step 4: Final Answer:
The mean of the numbers is 5.

Answer 2

The question asks for the arithmetic mean of the numbers 2, 4, 6, and 8. Let's check each option to see which one truly represents the average of this data set.

1. 4: This value is actually one of the numbers in the set itself. Since only one value (2) in the set is below 4, this number is too small to balance out the larger values 6 and 8, so it cannot be the mean.
2. 5: A quick check is to pair the extremes: \( 2 \) and \( 8 \) average to \( \frac{2+8}{2} = 5 \), and \( 4 \) and \( 6 \) average to \( \frac{4+6}{2} = 5 \). Since both pairs independently average to 5, the mean of the whole set must also be 5, matching the direct calculation \( \frac{2+4+6+8}{4} = \frac{20}{4} = 5 \).
3. 6: Testing 6 as the mean would require the total sum to equal \( 6 \times 4 = 24 \), but the actual sum of the numbers is only 20, so 6 is too large.
4. 8: This is simply the largest value in the set, not an average. Using 8 as the mean would require the sum to be \( 8 \times 4 = 32 \), far from the actual sum of 20.

The pairing method and the direct sum-and-divide calculation both confirm the same result for the average of these four numbers.

Therefore, the correct answer is 5.