Question

Which of the following is/are true for the data given below?

• A. Median is \(11\)
• B. Mode is \(11\)
• C. Median is \(14\)
• D. Mode is \(14\)

Hint:

Median is the middle value of ordered data, while mode is the value occurring with highest frequency.

Answer 1

The Correct Option is A, D

Step 1: Arrange the data in ascending order.
Given data:
\[ 15,\;8,\;10,\;6,\;11,\;9,\;15,\;7,\;14,\;5,\;17,\;14,\;8,\;14,\;12 \] Arranging in ascending order:
\[ 5,\;6,\;7,\;8,\;8,\;9,\;10,\;11,\;12,\;14,\;14,\;14,\;15,\;15,\;17 \]

Step 2: Count the number of observations.
Total number of observations is
\[ n=15 \] Since \(n\) is odd, median is the middle term.

Step 3: Find the median position.
Median position is given by
\[ \frac{n+1}{2} = \frac{15+1}{2} = 8 \] So, the median is the \(8^{th}\) term.

Step 4: Determine the median.
The \(8^{th}\) term in the ordered data is
\[ 11 \] Therefore,
\[ \text{Median}=11 \]
Hence, option (A) is correct and option (C) is incorrect.

Step 5: Find the mode.
Mode is the observation that occurs most frequently.
From the ordered data:
\[ 14 \text{ occurs } 3 \text{ times} \] \[ 15 \text{ occurs } 2 \text{ times} \] \[ 8 \text{ occurs } 2 \text{ times} \] All other values occur once.

Step 6: Determine the mode.
Since \(14\) occurs the maximum number of times,
\[ \text{Mode}=14 \] Hence, option (D) is correct and option (B) is incorrect.

Step 7: Final conclusion.
Thus, the correct statements are
\[ \boxed{\text{(A) and (D)}} \]