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The table above gives the age categories of the 161 employees at Compa

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The table above gives the age categories of the 161 employees at Compa  [#permalink]

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17 Jun 2016, 05:22
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The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49

Attachment:

2016-06-17_1621.png [ 21.26 KiB | Viewed 19471 times ]

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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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06 Dec 2016, 08:33
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Bunuel wrote:

The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49

We are given a table that has the age categories of the 161 employees at Company X and the number of employees in each category. Recall that if we have a set of n numbers arranged in order, the median of this set of n numbers is the number at the [(n + 1)/2]th position. Thus, the employee with the median age is at the (161+1)/2 = 162/2 = 81st position (assuming the ages of the employees are listed in order). The table provides us with the following information:

Age less than 20: 29 employees (i.e., 1st data point to 29th data point)

Age 20-29: 58 employees (i.e., 30th data point to 87th data point)

We see that the 81st data point will fall into the age group from 20-29 since this age group contains the 30th data point to the 87th data point.

Thus 20 ≤ m ≤ 29.

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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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17 Jun 2016, 07:25
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Total number of employees = 161. Thus the median of this set will be the 81st element. Now our job is to find out find range does this element belong to.

if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29". Thus the last element will 29 + 58 = 87th element of the set. And we are supposed to find out the 81st, which will lie in this range, Thus the answer is A.
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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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17 Jun 2016, 11:26
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FacelessMan wrote:
if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29".

Completely agree with the explanation , just thought about supplementing the highlighted part -

Attachment:

Capture.PNG [ 5.25 KiB | Viewed 17793 times ]

Drawing a cumulative chart will clear the confusion (if any )

Answer will definitely be (A)

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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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17 Jun 2016, 11:31
1
Abhishek009 wrote:
FacelessMan wrote:
if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29".

Completely agree with the explanation , just thought about supplementing the highlighted part -

Attachment:
Capture.PNG

Drawing a cumulative chart will clear the confusion (if any )

Answer will definitely be (A)

Don't you think the cumulative chart should be sorted in increasing order of the age - the other way around ? I know the answer will not change. But just asking.
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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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17 Jun 2016, 11:51
FacelessMan wrote:
Abhishek009 wrote:
FacelessMan wrote:
if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29".

Completely agree with the explanation , just thought about supplementing the highlighted part -

Attachment:
The attachment Capture.PNG is no longer available

Drawing a cumulative chart will clear the confusion (if any )

Answer will definitely be (A)

Don't you think the cumulative chart should be sorted in increasing order of the age - the other way around ? I know the answer will not change. But just asking.

That's perfect

Attachment:

Capture.PNG [ 5.34 KiB | Viewed 17754 times ]

Kudos to U...
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Thanks and Regards

Abhishek....

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The table above gives the age categories of the 161 employees at Compa  [#permalink]

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12 Sep 2017, 21:33

Bunuel Engr2012
The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

Can I not simply say that since maximum no of employees are in age bucket of 20-29 and median
is affected by cluster of data in middle in a set, (A) is the OA?
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Posts: 59588
Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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12 Sep 2017, 23:22
1

Bunuel Engr2012
The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

Can I not simply say that since maximum no of employees are in age bucket of 20-29 and median
is affected by cluster of data in middle in a set, (A) is the OA?

No.

The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
The median of a set with odd number of terms is the middle term when arranged in ascending (or descending) order.

The median age of 161 employees will be the age of 81st employee when the employees are arranged by age in ascending (or descending) order. The median age won't necessarily be from a group with the largest number of employees, for example, if the group less than 20 were 20, instead of 29 and the group 70 and over were 11, instead of 2, then the median age would be between 30 and 39 because 81st employee would fall in that group.

Hope it's clear.
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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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20 Nov 2019, 23:15
Hi Bunuel

Are there any similar frequency table questions to practice?

Thank you,
Dablu
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Posts: 59588
Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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20 Nov 2019, 23:37
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Re: The table above gives the age categories of the 161 employees at Compa  [#permalink]

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20 Nov 2019, 23:41
Thank you Bunuel. Really appreciate it!

Dablu
Re: The table above gives the age categories of the 161 employees at Compa   [#permalink] 20 Nov 2019, 23:41
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