For a recent workday, the graph displays the round-trip distance and m

Question

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 .

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Official Answer

Dropdown 1: x≤2 Dropdown 2: 10<x≤15

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Sajjad1994 · Accepted Answer

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.

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yashikaaggarwal · Answer

1. Walking median round trip => 30 people walked till distance ≤2 => 10 people walked till distance 2 6 people walked till distance 5 2 people walked till distance ≤2 => 18 people walked till distance 2 30 people walked till distance 5 26 people walked till distance 10 37 people walked till distance 15

Apt0810 · Answer

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.

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Kmohan1 · Answer

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

SatvikVedala · Answer

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

DrMock · Answer

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)

ManishaPrepMinds · Answer

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:
 
 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!

ShreyaMittal1609 · Answer

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

For a recent workday, the graph displays the round-trip distance and m

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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

GMAT Graphs and Tables (G&T) Questions

For a recent workday, the graph displays the round-trip distance and m

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

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My Rewards