Question

If the median of the following classified data is \(11\), find the value of \(a\) in the table.

• A. \(5\)
• B. \(6\)
• C. \(7\)
• D. \(5.5\)

Hint:

For grouped data, \[ \boxed{ \text{Median} = l+\frac{\left(\dfrac{N}{2}-cf\right)}{f}\times h } \] where:
• \(l\) = lower limit of median class,
• \(N\) = total frequency,
• \(cf\) = cumulative frequency before the median class,
• \(f\) = frequency of the median class,
• \(h\) = class width.

Answer 1

The Correct Option is A

Step 1: Identify the median class. Since the median is \(11\), the median class is \[ 10-15. \] Here, \[ l=10,\qquad h=5,\qquad f=a,\qquad cf=4+5=9. \] The total frequency is \[ N=4+5+a+3+3=a+15. \]

Step 2: Use the median formula. For grouped data, \[ \text{Median} = l+\frac{\left(\dfrac{N}{2}-cf\right)}{f}\times h. \] Substituting the given values, \[ 11 = 10+ \frac{\left(\dfrac{a+15}{2}-9\right)}{a}\times5. \]

Step 3: Solve for \(a\). \[ 1 = \frac{\left(\dfrac{a-3}{2}\right)}{a}\times5 \] \[ \frac{a-3}{2a} = \frac15 \] \[ 5(a-3)=2a \] \[ 5a-15=2a \] \[ 3a=15 \] \[ a=5. \]

Step 4: Final conclusion. \[ \boxed{a=5} \] Hence, the correct option is \(\boxed{(A)}\).