Question

(3.3.22) Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find Q3.
0.2
0.2
0.3
0.4
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
0.9
1.4
1.5
1.7
1.7
1.8
1.8
1.9
2.2
2.3
2.4
2.8
2.9
3.7
3.7
4.7
5.1
5.5
5.9
6.1
6.9
7.1
7.4
7.7
8.4
9.7
11.1
11.6
12.8
13.2
14.2
14.2
15.8
15.8
29.6
Q3= ? Mbps

Answer 1

$Q_3 = (\frac{3}{4}(n+1))^{th} \; value \; of \; the \; observation\\ n = 50 \\ Q_3 = \frac{3}{4}(50+1)^{th} \; value \; of \; the \; observation \\ = (\frac{3}{4}(51))^{th} \; value \; of \; the \; observation \\ = 38.25^{th} \; value \; of \; the \; observation \\ Q_3 = 38^{th} \; observation + 0.25(39^{th} - 38^{th}) = 2.9 + 0.25(3.7 - 2.9) \\ = 2.9 + 0.25 \times 0.8 \\ = 2.9+0.2 \\ = 3.1$

Answer: 3.1