Question

For a sample of 100 students, the median number of text messages sent per day is 90, the first quartile is 78, and the third quartile is 102. Select all of the answers that create a true statement.

Approximately 25 students in the sample send

more than 90 text messages.
less than 90 text messages.
more than 78 text messages.
more than 102 text messages.
between 90 and 102 text messages.
less than 78 text messages.
between 78 and 102 text messages.

Answer 1

Approximately 25 students send
Less than 78 text messages
More than 102 text messages

Answer 2

Answer with explanation:

$Q={\text{Median}}=90\\\\Q_{1}=78\\\\Q_{3}=102$

There are 100 students in the group.

If we divide 100 students into groups

→First quartile =25.5

means, first quartile of students has median value ≤ 78.

→Median =50.5

Most of the students sends ,90 messages a day.

→Third Quartile=75.5

Students lying above the third Quartile ,sends ≥102 messages per day.

First Quartile means, approximately 0- 25 students in the group , sends 78 messages.

$Q_{1}\leq 78$

Third Quartile means, 75-100 , students in the group, sends 102 messages .

$Q_{3}\geq 102$

Approximately 25 students in the sample send

1. more than 102 text messages.

2.less than 78 text messages.