Question

2.The number of tickets sold to a play for each showing is 78, 84, 87, 80, 91, 95, and 80.

Find the five-number summary for the data.

Answer 1

`Min =78`

The maximum is :

`Max = 95`

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

`Median =84`

Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:

`Q_1= (80+80)/(2)= 80`

Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:

`Q_3= (87+91)/(2)=89`

And finally the 5 number summary would be:

`Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96`

Explanation:

We have the following data given:

78, 84, 87, 80, 91, 95, and 80.

The first step is order the dataset on increasing way and we got:

78, 80,80, 84,87, 91, 95

We can begin finding the minimum value and for this case is:

`Min =78`

The maximum is :

`Max = 95`

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

`Median =84`

Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:

`Q_1= (80+80)/(2)= 80`

Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:

`Q_3= (87+91)/(2)=89`

And finally the 5 number summary would be:

`Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96`