Question

What will be the median of the given data of weight (in kg) ? \[ 70,\; 54,\; 45,\; 50,\; 68,\; 47,\; 75,\; 56,\; 55,\; 60,\; 72,\; 68,\; 66,\; 59,\; 57,\; 48 \]

• A. \(58\)
• B. \(60\)
• C. \(72\)
• D. \(56\)

Hint:

For an even number of observations, median is obtained by averaging the two middle observations after arranging the data in ascending order.

Answer 1

The Correct Option is A

Concept: The median is a measure of central tendency which represents: \[ \text{The middle value of an ordered data set} \] Rules for finding median:
• Arrange the observations in ascending order.
• If the number of observations \(n\) is odd: \[ \text{Median} = \left(\frac{n+1}{2}\right)^{th} \text{ observation} \]
• If \(n\) is even: \[ \text{Median} = \frac{\text{middle two observations}}{2} \]

Step 1: Writing the given observations. The given weights are: \[ 70,\; 54,\; 45,\; 50,\; 68,\; 47,\; 75,\; 56,\; 55,\; 60,\; 72,\; 68,\; 66,\; 59,\; 57,\; 48 \] Total number of observations: \[ n = 16 \] Since: \[ n = 16 \] which is an even number, we must find: \[ \text{Average of the 8th and 9th observations} \]

Step 2: Arranging the data in ascending order. After arranging: \[ 45,\; 47,\; 48,\; 50,\; 54,\; 55,\; 56,\; 57,\; 59,\; 60,\; 66,\; 68,\; 68,\; 70,\; 72,\; 75 \] Now identify: \[ 8^{th} \text{ and } 9^{th} \text{ observations} \] \[ 8^{th} = 57 \] \[ 9^{th} = 59 \]

Step 3: Calculating the median. Median: \[ = \frac{57+59}{2} \] \[ = \frac{116}{2} \] \[ = 58 \]

Step 4: Final conclusion. Therefore, the median of the given data is: \[ \boxed{58} \] Hence, the correct answer is: \[ \boxed{\text{(A) }58} \]