Answer to Question #216236 in Statistics and Probability for carla

Question

Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find

Upper Q 1

.

0.2

0.2

0.3

0.3

0.4

0.4

0.4

0.5

0.5

0.6

0.7

0.8

0.8

0.8

0.9

1.2

1.2

1.2

1.4

1.7

1.8

2.1

2.6

2.9

2.9

2.9

3.1

3.2

4.3

5.4

5.6

5.8

7.2

7.6

7.8

7.9

8.1

8.2

10.3

11.3

12.2

12.9

13.6

13.9

14.7

15.3

15.4

15.5

15.7

28.8

Upper Q 1

Answer 1

The data are in ascending order.

Compute the position (or rank) of the first quartile. 

Quartile Position $= \dfrac{(n+1)P}{100}= \dfrac{(50+1)\cdot25}{100}=12.75$

Since the position found is not integer, the method of interpolation needs to be used. The first quartile is located between the values in the positions 12 and 13.

Those values, based on the data organized in ascending order, are 0.8 and 0.8.

The value of 12.75 - 12 = 0.75 corresponds to the proportion of the distance between 0.8 and 0.8 where the quartile we are looking for is located at.

We compute

$$Q_1=0.8+0.75(0.8-0.8)=0.8$$

Compute the position (or rank) of the third quartile. 

Quartile Position $= \dfrac{(n+1)P}{100}= \dfrac{(50+1)\cdot75}{100}=38.25$

Since the position found is not integer, the method of interpolation needs to be used. The first quartile is located between the values in the positions 38 and 39.

Those values, based on the data organized in ascending order, are 8.2 and 10.3.

The value of 38.25 - 38 = 0.25 corresponds to the proportion of the distance between 8.2 and 10.3 where the quartile we are looking for is located at.

We compute

$$Q_3=8.2+0.25(10.3-8.2)=8.725$$

$Q_1=0.8$

$Q_3=8.725$