Answer to Question #147150 in Statistics and Probability for Vladimyr Lubin

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