The percentiles are: P40 = 33, P70 = 45, and P89 = 54.1, while the quartiles are Q1 = 28.5 and Q3 = 47.5
How to determine the percentiles?
The sorted dataset is:
22, 22, 24, 25, 26, 27, 27, 30, 30, 32,
33, 33, 35, 37, 38, 38, 40, 42, 44, 44,
45, 47, 48, 48, 49, 52, 55, 58, 62, 68
The number of data elements is:
N = 30
The 40th percentile (P40)
This is calculated using:
Element = (40% * N)th
So, we have:
Element = (40% * 30)th
Evaluate
Element = 12th
The 12th element is 33
Hence, the value of P40 is 33
The 70th percentile (P70)
This is calculated using:
Element = (70% * N)th
So, we have:
Element = (70% * 30)th
Evaluate
Element = 21st
The 21st element is 45
Hence, the value of P70 is 45
The 89th percentile (P89)
This is calculated using:
Element = (89% * N)th
So, we have:
Element = (89% * 30)th
Evaluate
Element = 26.7th
The element is calculated as:
Element = 26th + 0.7 * (27th - 26th)
So, we have:
Element = 52 + 0.7 * (55 - 52)
Element = 54.1
Hence, the value of P89 is 54.1
How to determine the quartiles?
The 1st quartile (Q1)
This is calculated using:
Element = (1/4 * N)th
So, we have:
Element = (1/4 * 30)th
Evaluate
Element = 7.5th
The element is calculated as:
Element = 7th + 0.5 * (8th - 7th)
So, we have:
Element = 27 + 0.5 * (30- 27)
Element = 28.5
Hence, the value of Q1 is 28.5
The 3rd quartile (Q3)
This is calculated using:
Element = (3/4 * N)th
So, we have:
Element = (3/4 * 30)th
Evaluate
Element = 22.5th
The element is calculated as:
Element = 22nd + 0.5 * (23rd - 22nd)
So, we have:
Element = 47 + 0.5 * (48- 47)
Element = 47.5
Hence, the value of Q3 is 47.5
The 5th quartile (Q5)
There is no such thing as Q5 i.e. the 5th quartile
Read more about quartiles and percentiles at:
https://brainly.com/question/20340210
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