Question

The weights of \(14\) children (in kg) are given below. Find the median weight of the children (in kg). \[ 47,\;39,\;46,\;32,\;50,\;43,\;44,\;45,\;37,\;36,\;48,\;42,\;41,\;40 \]

• A. \(42.0\)
• B. \(42.5\)
• C. \(43.0\)
• D. \(43.5\)

Hint:

For an even number of observations, \[ \boxed{ \text{Median} = \frac{\left(\frac{n}{2}\right)^{\text{th}} + \left(\frac{n}{2}+1\right)^{\text{th}}}{2} } \] after arranging the data in ascending order.

Answer 1

The Correct Option is B

Step 1: Arrange the observations in ascending order. \[ 32,\; 36,\; 37,\; 39,\; 40,\; 41,\; 42,\; 43,\; 44,\; 45,\; 46,\; 47,\; 48,\; 50 \] There are \[ n=14 \] observations.

Step 2: Locate the middle observations. Since \(n\) is even, the median is the average of the \[ \frac{n}{2}=7^{\text{th}} \] and \[ \left(\frac{n}{2}+1\right)=8^{\text{th}} \] observations. These are \[ 42 \quad \text{and} \quad 43. \]

Step 3: Calculate the median. \[ \text{Median} = \frac{42+43}{2} = 42.5. \]

Step 4: Final conclusion. \[ \boxed{42.5\text{ kg}} \] Hence, the correct option is \(\boxed{(B)}\).