Question

The mean of a dataset is 14 and the sum of the dataset is 84. How many numbers are in the dataset?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

Remember the triangular relationship: Sum at the top, Mean and Count at the bottom. Cover the value you want to find to see the formula. Cover Count, you get Sum / Mean. Cover Sum, you get Mean \(\times\) Count.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The mean (or average) of a dataset is calculated by dividing the sum of all the values by the number of values in the dataset. This question requires us to find the number of values, given the mean and the sum.
Step 2: Key Formula or Approach
The fundamental formula relating mean, sum, and count is:
\[ \text{Mean} = \frac{\text{Sum of Values}}{\text{Number of Values}} \] We can rearrange this formula to solve for the Number of Values:
\[ \text{Number of Values} = \frac{\text{Sum of Values}}{\text{Mean}} \] Step 3: Detailed Explanation
We are given the following information:
Mean = 14
Sum of Values = 84
Using the rearranged formula, we can find the number of values in the dataset:
\[ \text{Number of Values} = \frac{84}{14} \] \[ \text{Number of Values} = 6 \] Step 4: Final Answer
There are 6 numbers in the dataset.