Question

Suppose 300 nursing students took a certification test that is worth 100 points.

The five-number summary for the scores is shown here:


Minimum = 40; Q1 = 65; Median = 82; Q3 = 88; Maximum = 100


About how many students scored 65 or better?

About how many students scored 88 or better?

Answer 1

225 students scored 65 or better and 75 students scored 88 or better.

Explanation:

We are given that The five-number summary for the scores of 300 nursing students are given :

Minimum = 40

`Q_1 = 65`

Median = 82

`Q_3 = 88`

Maximum = 100

`Q_1` is the first quartile and is the median of the lower half of the data set. 25% of the numbers in the data set lie below
`Q_1` and about 75% lie above
`Q_1` .

`Q_3` is the third quartile and is the median of the upper half of the data set. 75% of the numbers in the data set lie below
`Q_3` and about 25% lie above
`Q_3`

i) .About how many students scored 65 or better?

`Q_1 = 65`

Since we know that 75% lie above
`Q_1` .

So, Number of students scored 65 or better =
`75\% * 300 = (75)/(100) * 300 =225`

ii)About how many students scored 88 or better?

`Q_3 = 88`

Since we know that 25% lie above
`Q_3`

So, Number of students scored 88 or better =
`25\% * 300 = (25)/(100) * 300 =75`

Hence 225 students scored 65 or better and 75 students scored 88 or better.