Question

The elements of the dataset \( \{-5, 1, a, 5, b\} \) are in ascending order. If both the mean and median of the dataset are equal to 3, what is the value of \( b \)?

• A. 7
• B. 11
• C. 9
• D. 12

Hint:

When working with datasets where both the mean and median are known, first use the median to find the middle element, then solve for the unknowns using the mean formula.

Answer 1

The Correct Option is B

Step 1: Median calculation 
The median of the dataset is the middle element. Since the dataset has 5 elements, the median will be the third element in the ordered set. Thus, \( a = 3 \) because the median is 3, and it corresponds to the third element. 
Step 2: Mean calculation 
The mean of the dataset is the sum of the elements divided by the number of elements. We are told that the mean is 3, so we can use the formula: \[ {Mean} = \frac{-5 + 1 + a + 5 + b}{5} = 3. \] Substituting \( a = 3 \) into the equation: \[ \frac{-5 + 1 + 3 + 5 + b}{5} = 3. \] Simplifying the equation: \[ \frac{4 + b}{5} = 3, \] \[ 4 + b = 15, \] \[ b = 11. \] Thus, the value of \( b \) is 11.