Question

Use the following cell phone data speeds (mbps) from a particular network. Find Q1

0.3,0.3,0.4,0.4,0.5,0.5,0.5,0.6,0.6,0.8
0.8,0.8,0.8,0.8,0.9,1.1,1.5,1.8,1.9,1.9
1.9,2.1,2.3,2.6,2.8,2.8,2.8,2.8,2.9,3.1
3.2,3.6,3.9,4.8,4.9,5.5,5.9,7.1,7.9,9.3
10.1,10.2,13.3,13.6,14.1,14.3,14.6,14.7,15.3,
30.9

Answer 1

Answer:

$Q_1=0.8$

Step-by-step explanation:

Given : Data 0.3,0.3,0.4,0.4,0.5,0.5,0.5,0.6,0.6,0.8,0.8,0.8,0.8,0.8,0.9,1.1,1.5,1.8,1.9,1.9,1.9  ,2.1,2.3,2.6,2.8,2.8,2.8,2.8,2.9,3.1,3.2,3.6,3.9,4.8,4.9,5.5,5.9,7.1,7.9,9.3, 10.1,10.2,13.3,13.6,14.1,14.3,14.6,14.7,15.3,30.9.

To find : Use the following cell phone data speeds (mbps) from a particular network to find $Q_1$ ?

Solution :

$Q_1$ is the median of lower data.

Total number of observation are 50 arranged in ascending order.

The median of even number is $\frac{n}{2}+1$ th term,

i.e.  $\frac{50}{2}+1=25+1=26$ th term

Before 26th term all term comes under lower fence.

i.e. 0.3,0.3,0.4,0.4,0.5,0.5,0.5,0.6,0.6,0.8,0.8,0.8,0.8,0.8,0.9,1.1,1.5,1.8,1.9,1.9,1.9,2.1,2.3,2.6,2.8. - 25 terms

The median of lower fence is

When n is odd, $\frac{n+1}{2}$ th term is median.

$\frac{25+1}{2}=\frac{26}{2}=13$ th term

13 th term of the data is 0.8.

Therefore, $Q_1=0.8$