Question

What is the median for the following set of data?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 0-5& 2\\ 5-10& 3\\ 10-15& 5\\ 15-20& 16\\ 20-25& 14\\ 25-30& 10\end{array}$$

• A. 19.69
• B. 15.67
• C. 20.11
• D. 11

Answer 1

The correct option is A 19.69

$\begin{array}{ccc}\mathrm{Median}& =& L+\frac{\left(}{\frac{N}{2}-C}\times h\\ N& =& 50\left(\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{frequencies}\right).\\ \frac{N}{2}& =& 25\\ & & \mathrm{So},\mathrm{The}\mathrm{median}\mathrm{class}\mathrm{is}15-20.\\ L& =& 15\left(\mathrm{Lower}\mathrm{value}\mathrm{of}\mathrm{median}\mathrm{class}\right).\\ f& =& 16\left(\mathrm{Frequency}\mathrm{of}\mathrm{median}\mathrm{class}\right).\\ C& =& 10(\mathrm{Cumulative}\mathrm{Frequency}\mathrm{till}\\ & & \mathrm{class}\mathrm{preceding}\mathrm{median}\mathrm{class}).\\ h& =& 5\left(\mathrm{Height}\mathrm{of}\mathrm{median}\mathrm{class}\right).\\ & & \\ \mathrm{Median}& =& 15+\frac{25-10}{16}\times 5\\ & =& 15+\frac{15}{16}\times 5\\ & =& 19.69\end{array}$