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For a recent workday, the graph displays the round-trip distance and m
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Updated on: 04 Feb 2024, 00:59
Updated on: 04 Feb 2024, 00:59
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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.
1. For all persons who travelled to work by walking, the median round-trip distance (x), in kilometres, satisfies the inequality .
2. 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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Re: For a recent workday, the graph displays the round-trip distance and m
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17 Apr 2021, 04:02
17 Apr 2021, 04:02
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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.
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General Discussion
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Re: For a recent workday, the graph displays the round-trip distance and m
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02 Jul 2020, 22:54
02 Jul 2020, 22:54
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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
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=> 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
