In the chart, the outer circle represents the age distribution of subs

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=74865 In the chart, the outer circle represents the age distribution of subscribers to Beautiful Garden magazine, and the inner circle represents the age distribution of subscribers to Garden Joy magazine. Neither magazine has any subscribers less than 18 years old. Select from the drop-down menus the options that complete the statement so that it is accurate based on the information provided. It can be determined from the chart that the GRAPH_1_PLACEHOLDER of the ages of the subscribers to Beautiful Garden is between 44 and 55 years, whereas that for subscribers to Garden Joy is between GRAPH_2_PLACEHOLDER years. Graph.jpg

chetan2u · Accepted Answer

You don’t have to assume anything.

The boundary between 65+(blue shaded) and 18-24 yr old(Grey shaded) is the start point. 
So when we move from this boundary clockwise towards 18+category, we start from 0% of people and end again at this boundary completing one circle covering entire 100% of subscribers.

Now exactly opposite to this line will be 50% mark and there is a wide dotted portion there. So 50% would lie in this dotted portion.

Saramoini · Answer

Hi, I hope you are fine.

The answer is not the mode because we don't have precise age data for each individual within the subgroups. Let’s consider two age groups that are so close in distribution: "45-54" and "55-64."

For example let's consider that for the group aged 45-54, we have 250 subscribers, divided equally among the ages 46 to 50 years:

50 subscribers aged 46 years 
 50 subscribers aged 47 years 
 50 subscribers aged 48 years 
 50 subscribers aged 49 years 
 50 subscribers aged 50 years

For the group aged 55-64, we also have 200 subscribers, but the distribution is heavily skewed towards one age:

150 subscribers aged 57 years 
 50 subscribers aged 58 years  
In this scenario, the mode is clearly 57 years, predominantly from the 55-64 age group. This illustrates why knowing the distribution within each age bracket is crucial. Without this, we might inaccurately assess the most common age. Each group represents an age range, and the exact number of individuals at each age within these ranges significantly influences the mode calculation.

Thus, it’s important to consider the internal age distribution within each group to accurately determine the mode. This example shows that the mode falls within the 55-64 age group, not the 45-54 group, highlighting the need for detailed demographic data in such analyses.

chetan2u · Answer

Be careful in reading the question stem.

It says the _Median_ of ages of the subscriber, and not median of age groups.

For median of ages, you have ti list ages in ascending/descending order and find middle age. Here, the ages are not given, but we know approx % in each group.

So, the age at 50% of the ages placed in order will give you the median.

How do you find that?
Take the boundary of 18-24 and 65+ as 0, so right diametrically opposite will give you 50% divider. Here, it lies in dotted portion, which gives 45-54 age bracket.

tickledpink001 · Answer

Thanks- but I thought listing the distribution of age groups (according to the number of people in each one) in ascending order gives the 50% mark (median) as the 2nd and 3rd age group so the ages should correspond to that group? so in this case 25-34 and 35-44 group?

chetan2u · Answer

Let me put the values in a different way
Age….%
0-10…1%
10-20…1%
20-30..1%
30-40..90%
40-50..7%

So, the median of ages would be in bracket 30-40 years.

Also, take there are 100 students, then the data will be 
Age….number
0-10…1
10-20…1
20-30..1
30-40..90
40-50..7

So ages in ascending order => 7, 15, 21, 31,31,31,32,32,32,32……..39,39,39,40, 41, 45
Of course the median will be between 30 and 40.

tickledpink001 · Answer

Let me put the values in a different way
Age….%
0-10…1%
10-20…1%
20-30..1%
30-40..90%
40-50..7%

So, the median of ages would be in bracket 30-40 years.

Also, take there are 100 students, then the data will be 
Age….number
0-10…1
10-20…1
20-30..1
30-40..90
40-50..7

So ages in ascending order => 7, 15, 21, 31,31,31,32,32,32,32……..39,39,39,40, 41, 45
Of course the median will be between 30 and 40.

thanks a tonne!

Q- what if in the pie chart, the segments weren't split according to size? how then would we figure out the median (instead of putting 0 at the smallest 2 sub groups)?

anikpait17 · Answer

I am not clear on how are we "assuming" what is the % of values present in a particular segement only by visualising. Yes the size of the segment does matter but I noticed most of the segments are almost very close in size to each other (like similar in size). Can anyone please put a simple explanation on this question?

KunalSawant08 · Answer

Why is the answer not mode?

tanishqgirotra · Answer

a really nice question!

egmat · Answer

Hi  KunalSawant08 
Thanks for posting your query.

Before finalizing the correct choice between Median and Mode for Blank 1, we must understand that whatever we mark here will affect our answer for Blank 2 as well.

Now, observe if you choose 'MODE' for blank 1, the question statement becomes "It can be determined from the chart that the  MODE  of the ages of the subscribers to Beautiful Garden is between 44 and 55 years, whereas  THE MODE  for subscribers to Garden Joy is between _____ years."
 
 We now need to determine, from the given age groups for Garden Joy magazine, which one has the MAXIMUM subscribers. 
 
 As the definition of Mode says, "The   mode   of a list of numbers is the number that occurs most often in the list."   
 If you observe, you will see that  it is impossible to say which portion of the inner circle is the BIGGEST , or we can say which age group has the maximum number of subscribers.
 
 See, the segments representing the age groups 25 to 34, 35 to 44, and 45 to 54 appear to be  roughly the same size . 
 It is impossible to assert that any one of these groups is larger than the others, without knowing the exact numbers.
 
  And as we have no guarantee of one of these age groups having more subscribers than the remaining two, we cannot find the  mode for Garden Joy magazine. 
 
 Now, while we cannot conclusively rule out "Mode," we should certainly look for a better option because if we have a better option available than this then that would be our DEFINITE answer, right!
 
 And See, we have Median as one of the options, so we must choose 'Median' over 'Mode' for Blank 1, as it can be determined for both magazines.  :)

Hope this will clarify!
Regards,
Aditi Gupta
Quant Expert, e-GMAT

egmat · Answer

Watch this solution to see how a seemingly complex question about mean, median, and mode in a pie chart can be tackled efficiently. This video demonstrates:
 
 The importance of drawing logical inferences from visual data 
 How to extract key information from a pie chart without getting bogged down in unnecessary calculations 
 The power of understanding the relationship between mean, median, and mode in different data distributions

https://www.youtube.com/watch?v=dLaEmQsg2rM

By focusing on these aspects, you'll learn to approach such questions strategically, potentially saving valuable time in the exam. Pay attention to how the solution leverages the visual nature of pie charts to make quick estimations. Can you spot the key visual cues that lead to the correct answer before the calculations are shown?

Ikemefuna2304 · Answer

I can't quite get why the correct interval is (34 - 45), when the graphic's interval is (35 - 44). I know it can be evident when you already figured out that we are talking about the median, but before that, the fact that the intervals are not the same, somehow confused me.

GMATinsight · Answer

Time to answer this question: 2:26 Mins

I started looking at the answer of first question here first.

The most appropriate answer looked like Mode for first one as it's clearly distinguishable as most occurring age group
However when I went to the second question then I faced challenge differentiating 45-54, 35-44 and 25-34

So I relooked at first question where I could be certain of something. Now, mean can NOT be calculated as it depends on exactness of ages hence eliminated cases were
Mean
Mode
So the correct answer of first was Median

Now, for the second question, Median was to be found by finding middle term when arranging in increasing order.

It was very clear when we start from 18-24, the blue part ie. 35-44 cuts more than half way hence the media

Dropdown 1: Median
Dropdown 2: 35-44

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tickledpink001

In the chart, the outer circle represents the age distribution of subscribers to Beautiful Garden magazine, and the inner circle represents the age distribution of subscribers to Garden Joy magazine. Neither magazine has any subscribers less than 18 years old.

Select from the drop-down menus the options that complete the statement so that it is accurate based on the information provided.

It can be determined from the chart that the of the ages of the subscribers to Beautiful Garden is between 44 and 55 years, whereas that for subscribers to Garden Joy is between years.

Show Spoiler

Attachment:

Graph.jpg

shisingh · Answer

I think the intervals are disjoint from each other in the graphic interval while median is joint so options are joint as well

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83913 --- Harsha GMAT-Club-Forum-r7xsfkyt.png

sb995 · Answer

Hi, can someone explain why the answer is not mean for the first blank? I understand why the correct answer is the median and the reasoning behind it but why not mean and how would we reason through that during the exam.

cheshire · Answer

Just looking at the graph you can see the answer is median so you wouldn't need to eliminate any options. Mean is tricky because we have a pie chart of ranges rather than integers.

Rhitib · Answer

Hello, can you explain me the question in a simple way? I selected mode, but I didn't know why it became wrong.

egmat · Answer

Hi Rhitib,

Good question, and it's a really common trap. Let me build on what Aditi (egmat) and Saramoini already said in the thread, but in the simplest way.

Think about what  mode  means: the single age that shows up  most often . To pick that from the chart, you'd have to point to one age band and say, "this band clearly has more subscribers than any other."

Reason 1 - you can't even find the biggest band.

Look at the inner ring (Garden Joy). The slices for  25-34 ,  35-44 , and  45-54  are all roughly the same size. By eye you cannot say which one is the largest. So there's no band you can confidently call the mode. (For Beautiful Garden it  looks  like  45-54 , but you need an answer that works for  both  magazines.)

Reason 2 - even the biggest band wouldn't give you the mode.

The chart only tells you how many people fall in each  range , not the exact ages inside it. The most common single age could sit in a  smaller  band.

Quick rehearsal with round numbers to feel Reason 2:

- Band  45-54  has  250  people, spread evenly across five ages - about  50  at each age.
- Band  55-64  has only  200  people, but  150  of them are exactly age  57 .

Here the bigger band is  45-54 , yet the  mode is 57 , which lives in the  smaller  band. So a big slice does not prove where the most common age is.

That's why mode is out and median is in.

The median just needs the age at the  50%  cumulative point - and you  can  find that from the ring by sweeping from the  18-24  /  65+  boundary until you cross halfway. It's determinable for both magazines; the mode is not.

Answer: Dropdown 1: median; Dropdown 2: 34 and 45

In the chart, the outer circle represents the age distribution of subs

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In the chart, the outer circle represents the age distribution of subs

Prep Toolkit

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