 It is currently 17 Nov 2019, 02:38 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # List X and list Y each contain 60 numbers. Frequency distrib  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 8760
Followers: 175

Kudos [?]: 2035 , given: 8089

List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
Expert's post 00:00

Question Stats: 78% (01:15) correct 21% (01:14) wrong based on 85 sessions
Attachment: #GREpracticequestion List X and list Y each contain 60 numbers..jpg [ 22.01 KiB | Viewed 1899 times ]

List X and list Y each contain 60 numbers. Frequency distributions for each list are given above. The average (arithmetic mean) of the numbers in list X is
2.7, and the average of the numbers in list Y is 7.1. List Z contains 120 numbers: the 60 numbers in list X and the 60 numbers in list Y.

 Quantity A Quantity B The average of the 120 numbers in list Z The median of the 120 numbers in list Z

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 2
Page: 150
Difficulty: medium
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Founder  Joined: 18 Apr 2015
Posts: 8760
Followers: 175

Kudos [?]: 2035  , given: 8089

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
3
KUDOS
Expert's post
Solution

This kind of question should be attacked with an upfront work. Students can be misleading by frequency or else. But dive into the problem and see the real gist of it

List Z is the sum of list X and Y. So the average of Z in the average of the single averages of X and Y : $$\frac{2.7+7.1}{2}=4.9$$

To compare the Average and the median, we have to calculate the median of Z. Z is composed of 120 numbers, so the median is the average of the two middle numbers.
X have numbers from 1 to 5, and Y from 6 to 9. As such, the two middle numbers of Z are 5 and 6. the median is $$\frac{6+5}{2}=5.5$$

So the correct answer is $$B$$
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern Joined: 24 May 2016
Posts: 33
Followers: 0

Kudos [?]: 10 , given: 22

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
why median is 5+6 .....not only 5 ??
they are not even numbers ? Retired Moderator Joined: 07 Jun 2014
Posts: 4808
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2278  , given: 393

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
Expert's post
awamy wrote:
why median is 5+6 .....not only 5 ??
they are not even numbers ?

Median is the exact mid point when a list of numbers are arranged in increasing order.

So in 1, 2, 3, 5, 7 median is 3.

But in 1, 2, 3, 5 median is $$\frac{2+3}{2}=2.5$$
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Intern Joined: 24 May 2016
Posts: 33
Followers: 0

Kudos [?]: 10  , given: 22

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
ohhh, yesss i didn't notice that there is no value (4)
thnx a lot for ur prompt reply
Manager Joined: 03 Dec 2017
Posts: 65
Followers: 0

Kudos [?]: 16 , given: 20

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
Carcass wrote:
Solution

This kind of question should be attacked with an upfront work. Students can be misleading by frequency or else. But dive into the problem and see the real gist of it

List Z is the sum of list X and Y. So the average of Z in the average of the single averages of X and Y : $$\frac{2.7+7.1}{2}=4.9$$

To compare the Average and the median, we have to calculate the median of Z. Z is composed of 120 numbers, so the median is the average of the two middle numbers.
X have numbers from 1 to 5, and Y from 6 to 9. As such, the two middle numbers of Z are 5 and 6. the median is $$\frac{6+5}{2}=5.5$$

So the correct answer is $$B$$

Hi Carcass,
Shouldn't the median be (6+6)/2= 6?
the median should be measure (order60+order61)/2
I apologized because I don't know how to explain better Retired Moderator Joined: 07 Jun 2014
Posts: 4808
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2278  , given: 393

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
Expert's post
wongpcla wrote:
Carcass wrote:

Hi Carcass,
Shouldn't the median be (6+6)/2= 6?
the median should be measure (order60+order61)/2
I apologized because I don't know how to explain better

Hi

The 60th term (order 60) has value 5 and and the 61st term (order 61) has value 6 so the median is average of both 5 and 6. Hence 5.5.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Intern Joined: 08 Mar 2018
Posts: 11
Followers: 0

Kudos [?]: 8  , given: 10

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
The answer should be B, I believe its keyed in incorrectly.
Thank you again for putting this together!! Intern Joined: 01 Oct 2018
Posts: 1
Followers: 0

Kudos [?]: 1  , given: 0

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
]
awamy wrote:
why median is 5+6 .....not only 5 ??
they are not even numbers ?

Median for odd number = (n+1/2)th
Median for even number = 1/2{(n/2)th+(n/2+1)th}
so, 5 and 6 are median Manager  Joined: 19 Nov 2018
Posts: 102
Followers: 0

Kudos [?]: 89  , given: 53

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
1
KUDOS
That is a clever solution, Carcass. I would just add for anyone who missed it, we can use the "average of the single averages" because each set has an equal number of values; in other words, their weight is equal. If the sets had unequal numbers of values, for example if the first set had 59 values and the second had 60, then we couldn't average the averages.

Having said this, when we come across a problem like this, where we can use your method it will save a lot of time, versus calculating a weighted mean, or just calculating a total sum for both sets using n and the mean (ex. 60x2.7 + 60x7.1) and then dividing to find the aggregate mean ( [60x2.7 + 60x7.1]/120 = 4.9).
Intern Joined: 18 Jul 2019
Posts: 32
Followers: 0

Kudos [?]: 2 , given: 2

Re: List X and list Y each contain 60 numbers. Frequency distrib [#permalink]
gat aach Re: List X and list Y each contain 60 numbers. Frequency distrib   [#permalink] 02 Oct 2019, 11:31
Display posts from previous: Sort by

# List X and list Y each contain 60 numbers. Frequency distrib  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.