The data set below represents the ages of 30 executives. Which ages are above the 75th percentile?
43
59 64
47
57
42
56
56
50
65
50
60
48
53
41
47
29
35
39
56
53
40
44
62
49
43
to 3
53
44
45
44
Determine the values in the data set above the 75th percentile. If a data value above the 75th percentile appears more than once in the data set.
make sure to include that value in your answer the appropriate number of times.
The ages above the 75th percentile are

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-10-20T12:28:59+02:00

Percentile is a measure of a dataset below which a percentage in its frequency distribution falls.

The ages above the 75th percentile are: 57, 59, 60, 62, 64 and 65

The sorted data is: 29 35 39 40 41 42 43 43 44 44 44 45 47 47 48 49 50 50 53 53 53 56 56 56 57 59 60 62 64 65

The 75th percentile is calculated using:

[tex]\mathbf{P_{75} = \frac{n }{100} \times 75}[/tex]

So, we have:

[tex]\mathbf{P_{75} = \frac{30 }{100} \times 75}[/tex]

[tex]\mathbf{P_{75} = 0.30\times 75}[/tex]

[tex]\mathbf{P_{75} = 22.50th}[/tex]

22.50 is halfway between 22 and 23

So, we have:

[tex]\mathbf{P_{75} = 22nd + 0.5(23rd - 22nd)}[/tex]

From the dataset; 22nd entry = 56; 23rd entry = 56

So, we have:

[tex]\mathbf{P_{75} = 56 + 0.5(56- 56)}[/tex]

[tex]\mathbf{P_{75} = 56}[/tex]

The 75th percentile is 56.

The ages above 56 are: 57, 59, 60, 62, 64 and 65

Hence, the ages above the 75th percentile are: 57, 59, 60, 62, 64 and 65