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:

$\mu=\frac{1}{N}\sum_{k\mathop{=}1}^na_k\cdot n_k$

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:

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

b)

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

$i=\frac{N}{2}=\frac{100}{2}=100$

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:

$\begin{gathered} Q_2=\frac{30+40}{2}=\frac{70}{2} \\ \\ \therefore Q_2=35\text{ minutes} \end{gathered}$