Question

Question 7. 5 points) Calculate the five number summary for the following box-and-whisker diagram. 5 6 15 7 8 9 10 10 0 Write your answers in increasing order.

Answer 1

We will put our data in ascending order first, as below.

`5\text{ 6 15 7 8 9 10 10 0 }\rightarrow0\text{ 5 6 7 8 9 10 10 15 }`

Five number summary are essentially five numbers that distinguish the given data, they are.

the sample minimum (smallest observation)

the lower quartile or first quartile

the median (the middle value)

the upper quartile or third quartile

the sample maximum (largest observation)

Let us calculate all of these in the data that we have been provided with.

(1) Median = mean of the two middle values, in this case, we have odd number of values, so we can take the middle three and take their average, therefore -> median = (7+8+9)/3 = 23/3

(2) Sample minimum = smallest number = 0

(3) Sample maximim = largest number = 15

(4) lower quartile = is the medain of the first group = (5+6)/2 = 11/2

(5) Upper quartile = median of the second group = (10+10)/2 = 10

therefore our five numbers are ,

0 11/2 23/3 10 15