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What is the median number of employees assigned per project
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What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Re: What is the median number of employees assigned per project
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04 May 2012, 01:46
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ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Not sufficient on its own.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Not sufficient on its own.
(1)+(2) Since 35% of of the projects have 2 or fewer (\(\leq{2}\))employees and 25% of the projects have 4 or more (\(\geq{4}\)) employees, then 100%-(25%+35%)=40% of the projects have exactly 3 employees assigned to each of them. So, the median number of employees assigned per project is 3. Sufficient.
Answer: C.
To elaborate more: consider there are 100 projects: \(\{p_1, \ p_2, \ ... , \ p_{100}\}\). The values of \(p_1\) to \(p_{35}\) will be 0, 1, or 2; the values of \(p_{36}\) to \(p_{75}\) will be exactly 3; the values of \(p_{76}\) to \(p_{100}\) will be 4 or more. \(Median=\frac{p_{50}+p_{51}}{2}=\frac{3+3}{2}=3\).
For example list can be: \(\{2, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 4, \ ..., \ (p_{100}=4)\}\); OR: \(\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (p_{100}=10000)\}\) (of course there are a lot of other breakdowns).
In any case median=3.
Hope it's clear.
P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
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Re: What is the median number of employees assigned per project
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20 Aug 2015, 13:36
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I've solved it this way (see attachment) -> the mid section of 40% =3 (it must be an integer, you cannot have fractions when dealing with persons So Statement 1+2 are sufficient (C)
What is the median number of employees assigned per project
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10 Dec 2012, 13:11
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What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
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11 Dec 2012, 02:47
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roygush wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Re: What is the median number of employees assigned per project
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11 Dec 2012, 03:43
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ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Ans: : Median is the middle value. Statements 1 and 2 alone give us insufficient data but when we combine both of them we see that 25 % have 4 or more and 35% have 2 or less therefore 40 %have 3 employees. Therefore the median would be 3 and the answer is (C).
Re: What is the median number of employees assigned per project
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27 Dec 2012, 08:24
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Bunuel wrote:
ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Not sufficient on its own.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Not sufficient on its own.
(1)+(2) Since 35% of of the projects have 2 or fewer (\(\leq{2}\))employees and 25% of the projects have 4 or more (\(\geq{4}\)) employees, then 100%-(25%+35%)=40% of the projects have exactly 3 employees assigned to each of them. So, the median number of employees assigned per project is 3. Sufficient.
Answer: C.
To elaborate more: consider there are 100 projects: \(\{p_1, \ p_2, \ ... , \ p_{100}\}\). The values of \(p_1\) to \(p_{35}\) will be 0, 1, or 2; the values of \(p_{36}\) to \(p_{75}\) will be exactly 3; the values of \(p_{76}\) to \(p_{100}\) will be 4 or more. \(Median=\frac{p_{50}+p_{51}}{2}=\frac{3+3}{2}=3\).
For example list can be: \(\{2, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 4, \ ..., \ (p_{100}=4)\}\); OR: \(\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (p_{100}=10000)\}\) (of course there are a lot of other breakdowns).
I Did not understand this. How can you deduce about the 40% of the projects based on the information given. The problem just says 25% of the projects have 4 or more. 35% of the projects have 2 or less. So it does not talk anything about 40%. 40 % can be 5,6,7 or anything right?? Could you explain it in detail.
Re: What is the median number of employees assigned per project
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27 Dec 2012, 09:37
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rajathpanta wrote:
Bunuel wrote:
ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Not sufficient on its own.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Not sufficient on its own.
(1)+(2) Since 35% of of the projects have 2 or fewer (\(\leq{2}\))employees and 25% of the projects have 4 or more (\(\geq{4}\)) employees, then 100%-(25%+35%)=40% of the projects have exactly 3 employees assigned to each of them. So, the median number of employees assigned per project is 3. Sufficient.
Answer: C.
To elaborate more: consider there are 100 projects: \(\{p_1, \ p_2, \ ... , \ p_{100}\}\). The values of \(p_1\) to \(p_{35}\) will be 0, 1, or 2; the values of \(p_{36}\) to \(p_{75}\) will be exactly 3; the values of \(p_{76}\) to \(p_{100}\) will be 4 or more. \(Median=\frac{p_{50}+p_{51}}{2}=\frac{3+3}{2}=3\).
For example list can be: \(\{2, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 4, \ ..., \ (p_{100}=4)\}\); OR: \(\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (p_{100}=10000)\}\) (of course there are a lot of other breakdowns).
I Did not understand this. How can you deduce about the 40% of the projects based on the information given. The problem just says 25% of the projects have 4 or more. 35% of the projects have 2 or less. So it does not talk anything about 40%. 40 % can be 5,6,7 or anything right?? Could you explain it in detail.
35 of the projects have 2 or fewer employees. 25 of the projects have 4 or more employees.
How many employees can be assigned to the remaining 40 projects? The ranges \(\leq{2}\) and \(\geq{4}\) are covered, thus the remaining 40 projects have 3 employees assigned to them.
Re: What is the median number of employees assigned per project
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13 Apr 2013, 02:02
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Aren't we assuming here that, statement 1 and 2 refer to highest 25 and bottom 35 percent of the employees, couldn't it be first 35 % then the next 25% and the remaining 40% with unknown number of employees per project, then the median will lie in 4 or more employees, we do not have any particular value and hence E as the correct answer.
Re: What is the median number of employees assigned per project
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13 Apr 2013, 02:14
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raxsin12 wrote:
Aren't we assuming here that, statement 1 and 2 refer to highest 25 and bottom 35 percent of the employees, couldn't it be first 35 % then the next 25% and the remaining 40% with unknown number of employees per project, then the median will lie in 4 or more employees, we do not have any particular value and hence E as the correct answer.
Statement 2 and 1 must refer to the bottom and to the highest part. "couldn't it be first 35 % then the next 25% and the remaining 40%"? NO. The first 35% have 2 or fewer (till here correct), but then your reasoning goes against the info in statement 1. What you are saying is that 25%+40%=65% has 4 or more employees => wrong, look at statement 1: (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
What is the median number of employees assigned per project
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18 May 2014, 09:57
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Bunuel, many thanks for your explanation.
One query : while considering median, we need to arrange the numbers in sequence, i guess.
If there are 20 projects, 1) 35% i.e. 7 projects have value as 4,5,6,7,8,8,8 2) 25% i.e. 5 projects have value as 1,2,2,2,0 3) 40% i.e. 8 projects have value as 3,3,3,3,3,3,3,3
So to derive the median, are we suppose to arrange the number in sequence i.e. ascending ?
What is the median number of employees assigned per project
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28 Nov 2015, 05:46
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Detailed Solution
Step-I: Given Info
The question asks us to find the median number of employees assigned per project for projects at Company Z, using the 2 statements given.
Step-II: Interpreting the Question Statement
To find the median number of employees, we need to somehow extract the central value for employees, when arranged in ascending order. Central value or median value will be the exact determination of value at the 50%th observation.
Step-III: Statement-I
Statement- I gives us the information about the 25% of projects have 4 or more employees assigned to each project. Now let us say we have 100 projects. There could be a possibility that remaining 75 projects (>50 projects) have 3 employees. Then the central observation (50%th observation- in this case 50th project value in total 100 projects) will have a median value of 3 employees. But the remaining 75 projects can have 2 employees as well. Then the median will be 2. So we cannot determine with exact surety, the exact value of median at 50%th observation.
Hence, statement 1 is not sufficient to answer the question.
Step-IV: Statement-II
Statement- II gives us information that 35% of the projects have 2 or fewer employees assigned to each project. Now, the remaining 65 projects (>50 projects) can have 3 employees. Then the central observation (50%th observation- in this case 50th project value in total 100 projects) will have a median value of 3 employees. But the remaining 65 projects(>50 projects) can have a median value of 4 employees as well. Then the median value will be 4 employees. So we cannot determine with exact surety, the exact value of median at 50%th observation.
Hence, statement 2 is not sufficient to answer this question.
Step-V: Combining Statements I & II
When we combine both the statements we know the value of 25% of projects (4 or more employees) and 35% projects(2 or fewer employees). So the remaining 40 projects (<50 projects) will have 3 employees. When the observations are arranged in ascending order. The first 35 observations will have 2 or fewer employees and next 40 observations will have 3 employees and then next 25 observations will have 4 or more employees. Thus, the median number of employees will be 3.
Hence, the exact determination of central value or value at 50%th observation is 3.
So the correct answer is C. Both the statements together are sufficient.
Key Takeaways
Use of concept of median and evaluating all possible value of central value (median value) for observations to be able to find exact value at 50%th observation (when values arranged in ascending order).
What is the median number of employees assigned per project
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13 Feb 2016, 03:39
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Dear Friends,
I need your help, coz I'm having problem I have two questions:
1) What if there is no project with THREE employees? Why can't 40% of projects have 5 or more employees or only 1 employee for that matter
2) I couldn't understand why 40% must be between 2 (35%) and 4 (25%): please see the attachment below. I would to know the reasoning behind why 3 employees (40%) must be between 2 and 4. The question does not say that 25% is at the higher band or that the 35% is at the lower band. (Although we can deduce 25% band is higher than the 35% band). Why can't the rest 100-(25+35)=40% be at an even higher band (eg 5 employees or more) ?
It hasn't been stated nowhere that 35% is the 1st and 25% is the last:
rohantiwari wrote:
1st 35% are either 1 or 2 and last 25% are 4 and above hence 35 - 75% should be 3
I would be so grateful, if u could explain me thoroughly. Thank you very much!
Bunuel wrote:
What is the median number of employees assigned per project for the projects at Company Z? (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Not sufficient on its own. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Not sufficient on its own. (1)+(2) Since 35% of of the projects have 2 or fewer (\(\leq{2}\))employees and 25% of the projects have 4 or more (\(\geq{4}\)) employees, then 100%-(25%+35%)=40% of the projects have exactly 3 employees assigned to each of them. So, the median number of employees assigned per project is 3. Sufficient. Answer: C. To elaborate more: consider there are 100 projects: \(\{p_1, \ p_2, \ ... , \ p_{100}\}\). The values of \(p_1\) to \(p_{35}\) will be 0, 1, or 2; the values of \(p_{36}\) to \(p_{75}\) will be exactly 3; the values of \(p_{76}\) to \(p_{100}\) will be 4 or more. \(Median=\frac{p_{50}+p_{51}}{2}=\frac{3+3}{2}=3\). For example list can be: \(\{2, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 4, \ ..., \ (p_{100}=4)\}\); OR: \(\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (p_{100}=10000)\}\) (of course there are a lot of other breakdowns). In any case median=3.
BrainLab wrote:
I've solved it this way (see attachment) -> the mid section of 40% =3 (it must be an integer, you cannot have fractions when dealing with persons So Statement 1+2 are sufficient (C)
hdwnkr wrote:
Each statement alone is insufficient Combining the two, we understand that there are three categories of employees. Group1: Less than 2 Group 2: Between 2 and 4 i.e. 3 Group 3: Greater than or equal to 4. The media falls in the mid - the 50th percent, which is group 2 Hence C, Both statements together are sufficient.
Zarrolou wrote:
Statement 2 and 1 must refer to the bottom and to the highest part. "couldn't it be first 35 % then the next 25% and the remaining 40%"? NO. The first 35% have 2 or fewer (till here correct), but then your reasoning goes against the info in statement 1. What you are saying is that 25%+40%=65% has 4 or more employees => wrong, look at statement 1: (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
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Re: What is the median number of employees assigned per project
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22 Feb 2016, 21:00
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studentsensual wrote:
Dear Friends,
I need your help, coz I'm having problem I have two questions:
1) What if there is no project with THREE employees? Why can't 40% of projects have 5 or more employees or only 1 employee for that matter
2) I couldn't understand why 40% must be between 2 (35%) and 4 (25%): please see the attachment below. I would to know the reasoning behind why 3 employees (40%) must be between 2 and 4. The question does not say that 25% is at the higher band or that the 35% is at the lower band. (Although we can deduce 25% band is higher than the 35% band). Why can't the rest 100-(25+35)=40% be at an even higher band (eg 5 employees or more) ?
It hasn't been stated nowhere that 35% is the 1st and 25% is the last:
rohantiwari wrote:
1st 35% are either 1 or 2 and last 25% are 4 and above hence 35 - 75% should be 3
I would be so grateful, if u could explain me thoroughly. Thank you very much!
Because "5 or more" is already a part of "4 or more" set.
Look, the number of employees assigned to a project could be any of the following: 0 (debatable but ok), 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... and so on
When you say 35% project have 2 or fewer employees assigned, it means that 25% projects have either 0 or 1 or 2 employees assigned. All projects that have 1 employee assigned to them are a part of this 25%. Say, this is the first group.
When you say 25% projects have 4 or MORE employees assigned, it includes all projects with 4 or 5 or 6 or 7 or 8 etc employees assigned to them. Any project that has 5 or more employees is already a part of this 25%. This is the second group.
So what about the rest of the 40% projects? Can they have 1 employee assigned? No. All those projects are accounted for in first group. Can they have 6 employees assigned? No. All those projects are accounted for in second group. The only number left that is not accounted for in wither group is 3. So 40% projects must have exactly 3 employees assigned.
Makes sense, now?
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Re: What is the median number of employees assigned per project
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01 Sep 2017, 14:00
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ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Target question: What is the median number of employees assigned per project?
Statement 1: 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Let's pretend that there are 4 projects altogether. There are several sets of values that meet this condition. Here are two: Case a: the set of numbers representing employees per project are {1, 1, 1, 4} in which case the median is 1 Case b: the set of numbers representing employees per project are {2, 2, 2, 4} in which case the median is 2 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Using logic similar to the above, we can show that statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined: 35% projects have 2 employees OR FEWER, and 25% of the projects have 4 employees OR MORE. So, 40% projects have EXACTLY 3 employees.
To find the median, we must find the middlemost value when all of the values are listed in ASCENDING order. So, the first 35% of the numbers will be 1's and 2's. Then next 40% of the numbers will be 3's And the last 25% of the numbers will be 4, 5's, etc
As you can see, the MIDDLEMOST value will be 3. In other words, the median must be 3. Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Re: What is the median number of employees assigned per project
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17 Jan 2018, 14:17
priyamne wrote:
ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Ans: : Median is the middle value. Statements 1 and 2 alone give us insufficient data but when we combine both of them we see that 25 % have 4 or more and 35% have 2 or less therefore 40 %have 3 employees. Therefore the median would be 3 and the answer is (C).
I understand that we're looking for the median and that each statement alone only tell us PART of what we want to know...further, I understand adding up both %s [25 & 35] and deducing that 40% have 3 employees. - HOWEVER, how do we know that 40% contains the median? What if we changed the numbers in Statement 1 & 2 both to 35? In this case, 30% would be left for 3 employees...how would this affect the answer?
Re: What is the median number of employees assigned per project
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18 Jan 2018, 07:16
LakerFan24 wrote:
priyamne wrote:
ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Ans: : Median is the middle value. Statements 1 and 2 alone give us insufficient data but when we combine both of them we see that 25 % have 4 or more and 35% have 2 or less therefore 40 %have 3 employees. Therefore the median would be 3 and the answer is (C).
I understand that we're looking for the median and that each statement alone only tell us PART of what we want to know...further, I understand adding up both %s [25 & 35] and deducing that 40% have 3 employees. - HOWEVER, how do we know that 40% contains the median? What if we changed the numbers in Statement 1 & 2 both to 35? In this case, 30% would be left for 3 employees...how would this affect the answer?
It won't change the answer. Say there are 20 projects. If 35% have 4 or more employees, it means 7 projects have 4 or more employees. If 35% have 2 or fewer employees, it means 7 projects have 2 or fewer employees. The leftover 30% i.e. 6 projects have 3 employees.
To find the median, you will need to arrange the number of employees in increasing order
Re: What is the median number of employees assigned per project
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23 Jan 2020, 01:38
Orange08 wrote:
Bunuel, many thanks for your explanation.
One query : while considering median, we need to arrange the numbers in sequence, i guess.
If there are 20 projects, 1) 35% i.e. 7 projects have value as 4,5,6,7,8,8,8 2) 25% i.e. 5 projects have value as 1,2,2,2,0 3) 40% i.e. 8 projects have value as 3,3,3,3,3,3,3,3
So to derive the median, are we suppose to arrange the number in sequence i.e. ascending ?
0,1,2,2,2,3,3,3,3,3,3,3,3,4,5,6,7,8,8
Is my understanding correct Bunuel?
If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order; If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.
So if there are 20 projects, 35% i.e. 7 projects have 2 or fewer employees assigned to each project, for example: 0, 0, 1, 1, 1, 2, 2; 40% i.e. 8 projects have exactly 3 employees assigned to each project: 3, 3, 3, 3, 3, 3, 3, 3; 25% i.e. 5 projects have 4 or more employees assigned to each project, for example: 4, 5, 6, 7, 8;