In a company, 58% of all its employees earn lesser than $50,000; 66% e

Question

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In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary?

A. 42000
B. 45000
C. 47500
D. 48000
E. 48550

uc26 · Answer

The median is the middle value of the set when the set is arranged in ascending or descending order. The only possibility based on the answer choices is a distribution where the median number of employees is an average of 45000+45000/2= 45,000.

Answer: B

Raxit85 · Answer

58 % of total earn < 50000 means 58th is earning 50000, 66% of total earn earn>40000. Means remaining 34 % earn earn to 40000. It indicates 34th is 40000. 
We can infer that 24 % of total earn from 40000 to 50000. If 17 % earn 45000 and 3% earn 48000, then 20% from 24% can be known. But we don’t know about 4% of 24%.

Case-I : 4% of 24% earns from 40000 to 45000.
34th = 40000, 34 to 38 earn between 40000 to 45000 and 38th = 45000.
So, 50th one, which is median, earns 45000.

Case-II : 0% earns from 40000 to 45000.
34th = 40000, 34 to 51 earn 45000.
So, 50th = 45000.

So, in both cases, median salary is 45000.
Imo. B

Archit3110 · Answer

let total employees be 200 so 58% of all its employees earn lesser than $50,000 i.e 116 employees <50,000 and 84 employees >50,000 66% earn more than $40,000 ; 132 employees >40,000 and 68 employees <40,000 exactly 17% earn $45,000; 3% earn $48,000 ; 34 earn 45,000 and 6 earn 48,000 116-68 ; 48 employees earn in range 40,000 to 50,000 also know that 34 earn 45,000 ( 17% ) and 6 (3%) earn 48,000 ; we can say that from 69th employee onwards each earn 45,000 and also 34 more earn same amount so total 48+34 ; upto 102nd employee would also earn 45,000 which would be covering the median value of 200 OPTION B In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary? A. 42000 B. 45000 C. 47500 D. 48000 E. 48550

yashikaaggarwal · Answer

0-40,000|40,000-50,000|50,000-100,000

40,000+ salary for 66% therefore people with 0-40,000 = 100-66% = 34%

50,000- salary for 58% therefore people with 50,000-100,000 = 100-58% = 42%

People with salary in between 40,000-50,000 = 24%
Let company have 100 people
And People with salary in between 40,000-50,000 = 24
Median salary will be of 50th people and 51th people.

Both lying in 40,000-50,000 category.

Namely 35,36,37,38,39......58
It's given 17% Or 17 people have 45000 salary.
& 3 people have 48000 salary

Let say people (58),(57),(56) have 48,000 salary
And the people with 45000 salary start thereafter. Namely 55,54,53,52..... 39

Therefore people 50&51 will have salary of 45000 each . Median = 50th + 51st/2
45000+45000/2 = 45000

Let say people 35,36,37,38,...... 51 have 45,000 salary
And the people with 48000 salary start thereafter. Namely 52,53,54

Therefore people 50&51 will again have salary of 45000 each . Median = 50th + 51st/2
45000+45000/2 = 45000

Answer is 45000
B option

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Gamerboyttt · Answer

B 
As 50th & 51st number is same 45k

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SohGMAT2020 · Answer

In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary?

A. 42000
B. 45000
C. 47500
D. 48000
E. 48550

Solution:

58% of all its employees earn lesser than $50,000: So, 0 to 58% of employees earn less than 50,000

66% earn more than $40,000: So, 100 to (100-66) or 34% of employees earn more than 40,000

So, 58%-34% of employees earn between 40000 and 50000. ie 24% of employees,

We are given information about 20% of these employees.

17% earn $45,000

3% earn $48,000

4% unknown

Now, if we consider the cases:

1. 4% greater than 48000, then

34% - 51% (17%) earn $45000
51% - 54% (3%) earn $48000
54% - 58% (4%) greater than 48000

Median = $45000

2. 4% lesser than $45000, then

34% - 38% (4%) earn lesser than $45000
38% - 55% (17%) earn $45000
55% - 58% (3%) earn $48000

Median = $45000

3. 4% between $45000 and $48000

34% - 51% (17%) earn $45000
51% - 55% (4%) between $45000 and $48000
55% - 58% (3%) earn $48000

Median = $45000

Since for all cases the median is $45000, the answer is B

HoneyLemon · Answer

B ,  IMO 
Since 
between 34 to 58 % people earn from 40K to 50K 
and 17% earn 45K . 
Hence the median must lie in 50 and 51% value 
i.e 45000 .

ashwini2k6jha · Answer

Answer:B
Let 100 be total number of employee
From given data ,we can deduce :
number of employees earn <40000 =38
number of employees earn 40000<()<50000 = 20 [17-45000 and 3- 48000)
number of employees earn >50000 = 46
For Median ,total number of employees=104
Median term= average of (52 th term+53 th term)=(45000+45000)/2=45000

ArunSharma12 · Answer

let the total employees be 100E.

58E earn less than 50,000, means 42E earn more than 50,000.
66E earn more than 40,000, means 34E earn less than 40,000.

between 50,000 and 40,000 there are 58E - 34E = 24E employess.

we know that 17E earn 45,000 and 3E earn 48,000.
so 24E - 20E = 4E earn some amount in between 50,000 and 40,000 but not 45,000 or 48,000.

34E + 17E = 51E; even if 4E earn something between 40,000 and 45,000 the median will still be in 45,000.
Ans: B

tejas29d · Answer

we can derive from thee question as follows:
42% earn more than 50k
3% earn 48k
17% earn 45k
34% earn less than 40k
so balance remaining 4% (100-42-3-17-34) lie between 40k to 50k. 
now irrespective of the salaries of these 4% people (i.e. even if they are more than 48k or between 48k and 45k or less than 45k) thy wont affect the median i.e. the 17% people having salary of 45k . thus 45k is the answer

Kinshook · Answer

Given; In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. Asked: What is the median salary? Screenshot 2020-06-07 at 11.20.56 AM.png 42% of the employees earn < $40,000 Irrespective of the earning of remaining 4% of the employees, median salary = $45,000 IMO B

coreyander · Answer

|-------a-------|---------b------|--------c------|-------d-----|-------e--------|
0................40k...............45k ...............48k.............50k ............ 100k

a+b+c+d+e = 100% ---(1)

We need to know the salary of 50th & 51st Percentile of the employee to find the median.

Given:   (i) 58% of all its employees earn lesser than $50,000;  
 --> a+b+c+d = 58% ----(2)
 ---> From (1) & (2),   e = 42%.

(ii) 66% earn more than $40,000  
 --> b+c+d+e = 66 ----(3)
 --> From (1) & (3),   a = 34%

Thus, eqn (1) can be written as  b+c+d=24%  ---(4)

We know 34 percentage get less than 40k. We need to know where the next 17 % people lie to find the median.  % in b will be crucial to this.

Given that 17% earn $45,000; 3% earn $48,000;

Thus from (4) & since 3% earn 48k, The Max and Min for b :  17 \leq b \leq 21 .  (17% earn 45k....24-3=21%)

Case I: b=17, then 34% --> 0 to 40k
----------------------17% exactly 45k.
----------------------Thus, 50 & 51 percentile are 45k. 
---------------------- Median 45k.

Case II: b=21, then 34% --> 0 to 40k.
------------------------4% --> 40 to 44.9k..................  (21-17=4%...... 17% is exactly in 45k ) 
-----------------------And the next 17% exactly 45k......  (i.e. 38. to 55 percentile is 45k. )
  Median is still 45k. Since, 50 & 51 percentile are 45k.  
 
 Thus, answer is (B) 45000

In a company, 58% of all its employees earn lesser than $50,000; 66% e

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