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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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tickledpink001 wrote:
chetan2u wrote:
tickledpink001 wrote:
Can anyone please help me understand how the median of the ages of the "beautiful garden" group is between 44 and 55 years?
The median of the 6 age groups, when listen in ascending order, should be between the 3rd and 4th2 group by size- in this case it's the 25-34 and 35-44 group- where am I going wrong?



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.


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?



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.
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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.[/quote]

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)?
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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Hello tickledpink001 please provide all the answer options of both the blanks. I will format the question.

Thank you
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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?
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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anikpait17 wrote:
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?



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.
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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Why is the answer not mode?
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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a really nice question!
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In the chart, the outer circle represents the age distribution of subs [#permalink]
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KunalSawant08 wrote:
Why is the answer not mode?

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.­
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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KunalSawant08 wrote:
Why is the answer not mode?

­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 ­
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Re: In the chart, the outer circle represents the age distribution of subs [#permalink]
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