Chapter 4, Problem 13PT1

To determine

To find out the median of the given frequency table of the patients.

Answer to Problem 13PT1

The option b) is correct.

Explanation of Solution

The frequency table is given below summarizes the times in the last month that patients at the emergency room of small-city hospital waited to receive medical attention:

Class Interval	x	f	c.f.	f.x.
<10	5	5	5	25
10-20	15	24	29	360
20-30	25	45	74	1125
30-40	35	38	112	1330
40-50	45	19	131	855
50-60	55	7	138	385
60-70	65	2	140	130
Total		N=140		4210

Mean

  $\begin{array}{l}=\frac{{\displaystyle \sum _{i=1}^n{f}_i{x}_i}}{{\displaystyle \sum _{i=1}^n{f}_i}}\\ =\frac{4210}{140}\\ =30.071\\ =30\text{ minutes}\end{array}$

Median

  $\begin{array}{l}=l+\frac{h}{2}\left(\frac{N}{2}-c\right)\\ =20+\frac{10}{45}\left(\frac{140}{2}-29\right)\\ =29.11\\ =29\text{ minutes}\end{array}$

Hence the correct option is (b).