SOLUTION: The following are the annual salaries of 22 chief executive officers of major companies (The salaries are written ir thousands of dollars) 785, 152, 176, 89, 80, 537, 514, 333,

Question 1202358: The following are the annual salaries of 22 chief executive officers of major companies (The salaries are written ir
thousands of dollars)
785, 152, 176, 89, 80, 537, 514, 333, 581, 628, 671, 738, 447, 423, 210, 230, 695, 490, 1103, 604, 345, 540.
Find the 25th and 70th percentile of these salaries.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Unfortunately percentiles do not have a standard agreed upon definition.
Sources:
https://www.statisticshowto.com/probability-and-statistics/percentiles-rank-range/#:~:text=but%20there%20is%20no%20universal%20definition%20for%20it
and
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Lane)/01%3A_Introduction_to_Statistics/1.07%3A_Percentiles#:~:text=There%20is%20no%20universally%20accepted%20definition%20of%20a%20percentile

Despite this glaring flaw, I'll be using the formulas mentioned on this page
https://www.calculatorsoup.com/calculators/statistics/percentile-calculator.php
That page also provides a calculator to verify the answer.

Original data set = {785, 152, 176, 89, 80, 537, 514, 333, 581, 628, 671, 738, 447, 423, 210, 230, 695, 490, 1103, 604, 345, 540}

Sorted data set = {80, 89, 152, 176, 210, 230, 333, 345, 423, 447, 490, 514, 537, 540, 581, 604, 628, 671, 695, 738, 785, 1103}

n = number of items in the set
n = 22

Let's list each value with its associated rank.

Score	Rank
80	1
89	2
152	3
176	4
210	5
230	6
333	7
345	8
423	9
447	10
490	11
514	12
537	13
540	14
581	15
604	16
628	17
671	18
695	19
738	20
785	21
1103	22

Then,
rank = (percentile/100)*(n - 1) + 1
rank = (25/100)*(22 - 1) + 1
rank = 6.25

integer part = x = 6
fractional part = y = 0.25

The scores at ranks 6 and 7 are 230 and 333 respectively. Refer to the table above. Let's call these scores P and Q.

And finally,
P + y*(Q - P)
230 + 0.25*(333 - 230)
255.75
is the 25th percentile.

Again, there is no agreed upon universal definition of percentile.
If your stats textbook uses another definition, then be sure to use that.

------------------------------------

Now let's find the 70th percentile
rank = (percentile/100)*(n - 1) + 1
rank = (70/100)*(22 - 1) + 1
rank = 15.7

x = integer part = 15
y = fractional part = 0.7

The values at ranks 15 and 16 are 581 and 604 in that order.
P = 581
Q = 604

P + y*(Q - P)
581 + 0.7*(604 - 581)
597.1
That represents the 70th percentile.
About 70% of the scores are below this cutoff point.

RELATED QUESTIONS
The following are the annual salaries of 19 chief executive officers of major companies.... (answered by Boreal)

Please help me with this problem; Thank you ahead of time. The following data are the... (answered by mathmate)

Fifty chief executive officers of small to medium-sized companies were classified... (answered by ewatrrr)

The monthly salaries of... (answered by ikleyn)

The police department of a major city has found that the average height of their 1,250... (answered by ewatrrr)

The salaries of a secretary, a salesperson, and a vice president for a retail sales... (answered by josgarithmetic)

1.The following salaries (in pesos) were obtained from a sample of 12 executive... (answered by Glaviolette,math_tutor2020)

A group of 150 randomly selected chief executive officers (CEO�s) were tested for... (answered by Fombitz)

The salaries of A, B, C are in the ratio 2:3:5. if the increment of 15%, 10% and 20% are... (answered by ankor@dixie-net.com)