Question

Which statement is correct assuming that \(a\) represents the range, \(b\) represents the mean, \(c\) represents the median, and \(d\) represents the mode for the number set: 8, 3, 11, 12, 3, 4, 6, 15, 1 ?

• A. \(a<c<d<b\)
• B. \(d<c<b<a\)
• C. \(b = c<a<d\)
• D. \(c<b<a<d\)
• E. \(b<c<a = d\)

Hint:

Always compute mode, median, mean, and range carefully, then compare numerically to form inequalities.

Answer 1

The Correct Option is B

Step 1: Arrange the numbers in ascending order.
1, 3, 3, 4, 6, 8, 11, 12, 15.
Step 2: Calculate range.
\(a = 15 - 1 = 14\).
Step 3: Find mean.
Sum = 63. Mean = \( \frac{63}{9} = 7\). So, \(b = 7\).
Step 4: Find median.
Middle element (5th) = 6. So, \(c = 6\).
Step 5: Find mode.
Most frequent number = 3. So, \(d = 3\).
Step 6: Order them.
\(d = 3<c = 6<b = 7<a = 14\).
Final Answer: \[ \boxed{d<c<b<a} \]