Question

How can I calculate the mean waiting per time . per child? How do I calculate the median of the distribution?

Answer 1

a)

The mean waiting time per child can be calculated using the formula:

`\mu=(1)/(N)\sum_{k\mathop{=}1}^na_k\cdot n_k`

Where a_k is the time, n_k is the number of children for time k, and N is the total number of children. Using the data from the problem:

`\begin{gathered} \mu=(10\cdot40+20\cdot50+30\cdot10+40\cdot70+50\cdot0+60\cdot30)/(40+50+10+70+0+30) \\ \\ \mu=(400+1000+300+2800+0+1800)/(200)=(6300)/(200) \\ \\ \therefore\mu=31.5\text{ minutes} \end{gathered}`

b)

For the median, we calculate the tentative position of the median using the equation:

`i=(N)/(2)=(100)/(2)=100`

Since this is an integer number, the real median is the semi-sum of the elements at positions i and (i+1). From the table, these elements are 30 and 40, so the median is:

`\begin{gathered} Q_2=(30+40)/(2)=(70)/(2) \\ \\ \therefore Q_2=35\text{ minutes} \end{gathered}`