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For a recent workday, the graph displays the round-trip distance and mode of travel for all persons travelling to work in a medium-sized city.
From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
For all persons who travelled to work by walking, the median round-trip distance (x), in kilometres, satisfies the inequality .
For all persons who travelled to work by public transit, the median round-trip distance (x), in kilometres, satisfies the inequality .
The last two questions based on this stem can be found here.
njnj.jpg [ 59.47 KiB | Viewed 25286 times ]
From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
For all persons who travelled to work by walking, the median round-trip distance (x), in kilometres, satisfies the inequality .
For all persons who travelled to work by public transit, the median round-trip distance (x), in kilometres, satisfies the inequality .
The last two questions based on this stem can be found here.
Attachment:
njnj.jpg [ 59.47 KiB | Viewed 25286 times ]
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Posts: 16,416
Official Explanation
RO1
The median round-trip distance of the walkers can be found by first determining from the bar graph how many people walked each distance. The results are recorded in the table:
The total number of people walking is 30 + 10 + 6 = 46. Since 46 is an even number, the median distance walked will be the average (arithmetic mean) of the distance walked by the 23rd and 24th walkers, when the distances are listed from least to greatest. Because 30 people walked a distance less than or equal to 2 km, both the 23rd and 24th walkers will be included in this group. Thus, the median is within the distance range d ≤ 2, since the average of two numbers that are less than or equal to 2 will be a number less than or equal to 2.
The correct answer is x ≤ 2.
RO2
Using the method described in the analysis of RO1, the approximate numbers of people traveling each distance by public transit are recorded in the table:
The total number of people taking public transit is 2 + 17 + 30 + 17 +37 = 103. Since 103 is an odd number, the median distance traveled will be that of the middle traveler (the 52nd) when the distances are listed in order. Counting the number of travelers from least to greatest, there are 2 + 17 + 30 = 49 travelers for whom d ≤ 10. Thus, the distance traveled by the 52nd traveler is 10 < d ≤ 15.
The correct answer is 10 < x ≤ 15.
RO1
The median round-trip distance of the walkers can be found by first determining from the bar graph how many people walked each distance. The results are recorded in the table:
The total number of people walking is 30 + 10 + 6 = 46. Since 46 is an even number, the median distance walked will be the average (arithmetic mean) of the distance walked by the 23rd and 24th walkers, when the distances are listed from least to greatest. Because 30 people walked a distance less than or equal to 2 km, both the 23rd and 24th walkers will be included in this group. Thus, the median is within the distance range d ≤ 2, since the average of two numbers that are less than or equal to 2 will be a number less than or equal to 2.
The correct answer is x ≤ 2.
RO2
Using the method described in the analysis of RO1, the approximate numbers of people traveling each distance by public transit are recorded in the table:
The total number of people taking public transit is 2 + 17 + 30 + 17 +37 = 103. Since 103 is an odd number, the median distance traveled will be that of the middle traveler (the 52nd) when the distances are listed in order. Counting the number of travelers from least to greatest, there are 2 + 17 + 30 = 49 travelers for whom d ≤ 10. Thus, the distance traveled by the 52nd traveler is 10 < d ≤ 15.
The correct answer is 10 < x ≤ 15.
Attachment:
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General Discussion
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 18 Jan 2020
Last visit: 10 Aug 2026
Posts: 3,095
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,095
1. Walking median round trip
=> 30 people walked till distance ≤2
=> 10 people walked till distance 2<X≤5
=> 6 people walked till distance 5<X≤10 = 46 units.
Median = 23&24 value..
Which lies in X≤2
Answer is A
2) Public Transit median round trip
=> 2 people walked till distance ≤2
=> 18 people walked till distance 2<X≤5
=> 30 people walked till distance 5<X≤10
=> 26 people walked till distance 10<X≤15
=> 37 people walked till distance 15<X = 113 units.
Median = 57 value..
Which lies in 10<X≤15
Answer is C
3) For round-trip distances less than or equal to 10 km, the number of persons traveling to work by walking = 30+10+6 = 46 units
For round-trip distances less than or equal to 10 km, the number of persons traveling to work by bicycling = 34+50+40 = 124 units
No. Of people walking is less than bicyclers.
Answer is A
4) For round-trip distances less than or equal to 10 km, the number of persons traveling to work by car = 9+20+28 = 57 units
For round-trip distances less than or equal to 10 km, the number of persons traveling to work by public transit = 2+18+30 = 50 units
No. Of people travelling by car is greater than public transiters.
Answer is C
Posted from my mobile device
_________________
=> 30 people walked till distance ≤2
=> 10 people walked till distance 2<X≤5
=> 6 people walked till distance 5<X≤10 = 46 units.
Median = 23&24 value..
Which lies in X≤2
Answer is A
2) Public Transit median round trip
=> 2 people walked till distance ≤2
=> 18 people walked till distance 2<X≤5
=> 30 people walked till distance 5<X≤10
=> 26 people walked till distance 10<X≤15
=> 37 people walked till distance 15<X = 113 units.
Median = 57 value..
Which lies in 10<X≤15
Answer is C
3) For round-trip distances less than or equal to 10 km, the number of persons traveling to work by walking = 30+10+6 = 46 units
For round-trip distances less than or equal to 10 km, the number of persons traveling to work by bicycling = 34+50+40 = 124 units
No. Of people walking is less than bicyclers.
Answer is A
4) For round-trip distances less than or equal to 10 km, the number of persons traveling to work by car = 9+20+28 = 57 units
For round-trip distances less than or equal to 10 km, the number of persons traveling to work by public transit = 2+18+30 = 50 units
No. Of people travelling by car is greater than public transiters.
Answer is C
Posted from my mobile device
_________________
1)A,since there are total 47 values in the category of people walking round the trip and the median would be roughly around at the value = 24,which lies in x<=2.
2)C,since people going via public transit in different ranges are:
x<=2 ---2
2<x<=5---18
5<x<=10---30
10<x<=15---26
x>15---37
So here Median = 57,which lies in 10<x<=15
3)A,For round-trip distances <= 10 km, the number of people traveling to work by walking = 30+10+6 = 46 units
For round-trip distances<= 10 km, the number of people traveling to work by bicycling = 34+50+40 = 124 units.No. Of people walking is less than bicycles
4)C,For round-trip distances<= 10 km, the number of people traveling to work by car = 9+20+28 = 57 units
For round-trip distance <=10 km, the number of people traveling to work by public transit = 2+18+30 = 50 units
So,No. Of people travelling by car is greater than public transiters.
Posted from my mobile device
2)C,since people going via public transit in different ranges are:
x<=2 ---2
2<x<=5---18
5<x<=10---30
10<x<=15---26
x>15---37
So here Median = 57,which lies in 10<x<=15
3)A,For round-trip distances <= 10 km, the number of people traveling to work by walking = 30+10+6 = 46 units
For round-trip distances<= 10 km, the number of people traveling to work by bicycling = 34+50+40 = 124 units.No. Of people walking is less than bicycles
4)C,For round-trip distances<= 10 km, the number of people traveling to work by car = 9+20+28 = 57 units
For round-trip distance <=10 km, the number of people traveling to work by public transit = 2+18+30 = 50 units
So,No. Of people travelling by car is greater than public transiters.
Posted from my mobile device
The median is based on the ordered list of observations.
For blank 1, the total number of people who walk is ~45. The median will be 23th observation. So, x<=2
For bank 2, the total number of people who use the public transit is ~113. The median will be ~57th observation. Which will be in the range 10<x<=15
For blank 1, the total number of people who walk is ~45. The median will be 23th observation. So, x<=2
For bank 2, the total number of people who use the public transit is ~113. The median will be ~57th observation. Which will be in the range 10<x<=15
Posts: 168
Steps to follow
1. Calculate the no.of observations
2. Find median observation based on total observations (even or odd)
3. Go back & arrange the observations in ascending order (30(x<= 2)...10(2<x<=5)...6(5<x<=10))
4. Find the range where median observation falls
1. Calculate the no.of observations
2. Find median observation based on total observations (even or odd)
3. Go back & arrange the observations in ascending order (30(x<= 2)...10(2<x<=5)...6(5<x<=10))
4. Find the range where median observation falls
I generally have trouble reading what value's median we're calculating. Is there something fundamental I need to understand? In this case, I was a little confused between arranging it as Q1: (0, 0, 7, 10, 30) or total/number and then find the middle values (correct answer)
Posts: 139
Let’s clear up a small confusion — it’s totally normal to mix this up at first!
You wrote: (0, 0, 7, 10, 30) and took the median as 7.
It looks like you were trying to find the median of the group totals, thinking of them as if they were individual data points — like 0 people, 0 people, 7 people, etc.
But here’s the key idea:
These numbers (0, 0, 7, 10, 30) just tell us how many people are in each distance group — they’re frequencies, not actual distances walked by individual people.
What We Actually Need to Do:
We want the median distance walked, which means:
Total = 47,000 people
Median = 24000th person (since median is the middle value).
Now, the 24000thperson falls in the first group (≤ 2 km)
So the median distance is ≤ 2 km.
Fundamental Rule to Remember:
When calculating the median from grouped data, we are looking at the position of each individual person, not the groups themselves.
Hope this helps!
You wrote: (0, 0, 7, 10, 30) and took the median as 7.
It looks like you were trying to find the median of the group totals, thinking of them as if they were individual data points — like 0 people, 0 people, 7 people, etc.
But here’s the key idea:
These numbers (0, 0, 7, 10, 30) just tell us how many people are in each distance group — they’re frequencies, not actual distances walked by individual people.
What We Actually Need to Do:
We want the median distance walked, which means:
- Arrange all individual people (not groups) by how far they walked.
- Find the middle person in that lineup.
| Distance walked (km) | No. of people (in thousands) | Cumulative total |
|---|---|---|
| ≤ 2 km | 30 | 30 |
| 2 < d ≤ 5 km | 10 | 40 |
| 5 < d ≤ 10 km | 7 | 47 |
| 10 < d ≤ 15 km | 0 | 47 |
| > 15 km | 0 | 47 |
Total = 47,000 people
Median = 24000th person (since median is the middle value).
Now, the 24000thperson falls in the first group (≤ 2 km)
So the median distance is ≤ 2 km.
Fundamental Rule to Remember:
When calculating the median from grouped data, we are looking at the position of each individual person, not the groups themselves.
Hope this helps!
DrMock
GMAT Focus 1: 545 Q77 V77 DI77 
Posts: 82
Hi Bunuel ManishaPrepMinds
Did the mistake of approximation. Counted total pubic transit as 100 instead of 103- which led to the wrong distance range.
In real exam also are options so close in G&T questions or other questions?
2) Public Transit median round trip
=> 2 people walked till distance ≤2
=> 18 people walked till distance 2<X≤5
=> 30 people walked till distance 5<X≤10
=> 15 people walked till distance 10<X≤15
=> 35 people walked till distance 15<X = 100 units.
Median = 50 value..
Which lies in 5<X≤10
Did the mistake of approximation. Counted total pubic transit as 100 instead of 103- which led to the wrong distance range.
In real exam also are options so close in G&T questions or other questions?
2) Public Transit median round trip
=> 2 people walked till distance ≤2
=> 18 people walked till distance 2<X≤5
=> 30 people walked till distance 5<X≤10
=> 15 people walked till distance 10<X≤15
=> 35 people walked till distance 15<X = 100 units.
Median = 50 value..
Which lies in 5<X≤10
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