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1. Yes
Direct one, as we can see the Tire failures per 1000 landing for Pro Elite:
5.2,6,6.5,6.8,6.9. The median for the set is 6.5 which is of Hero Airlines.
So 1st is true as can be inferred from the data.

2. No.
It can also be directly inferred using the data in the table.
The airline that had the longest average maintenance interval is Boulder Air (30, 7.1) but the airline that had the greatest tire age is Mystic Airways(28,9).

3. No.
The tire brand with the highest average failures per 1000 landings across all is Maximum Air(8.3) and the airline that had the greatest tire age is Mystic Airways(9), so no they are not same.
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Pretty straight forward...Not sure why the difficulty level has been set so high for this question.­
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Let me try to explain statement (3)
"The tire brand with the highest average failures per 1000 landings across all reporting airlines also had the highest average tire age across all reporting airlines."

Part1
The tire brand with the highest average failures per 1000 landings across all reporting airlines:
Let's take all 3 brands:
FUTURE: [(6.3*1000)+(6.9*1000)]/2000 = 6.6
Grizzly Plus: [(6.8*1000)+(8.3*1000)+(7.5*1000)]/3000 = 7.53
Pro Eite: [(6*1000)+(6.8*1000)+(6.9*1000)+(6.5*1000)+(5.2*1000)]/5000 = 6.28
"we can calculate this as we know each average is calculated for 1000 landings"
In the case if each airlines/brands have different number of landings and we are unaware of the landings number, In such case it is not possible to calculate average for each brand

Part2
and that tire brand has the highest average tire age across all reporting airlines.­

We cant say that the Brand "Grizzly Plus" has highest average tire age BECAUSE
"We are unaware of number of tires purchased by each airlines; number of tires purchased by each airlines may be differnet and that mentioned average is also calculated based on that number of tire purchase"
eg:
Maximum air: no. of tires purchased is 1000 and average tire age is 7.5
Mystic Airways: no. of tires purchased is 1 and average tire age is 9

In this case, Average tire age of the Brand "Grizzly Plus" would be : approx 7.5  (and we can't say it is the highest as other brands have maximum average of 7.8 and 8.1)
"We are unaware of number of tires purchased by both the airlines using brand "Grizzly Plus"

Please feel free to give kudos if the explaination helps you.
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­The tire brand with the highest average failures per 1000 landings across all reporting airlines also had the highest average tire age across all reporting airlines."

Calculate the average tire failures and tire age for each brand:


  • Future


    • Average tire failures: (6.3 + 5.9) / 2 = 6.1
    • Average tire age: (6.4 + 7.8) / 2 = 7.1
  • Grizzly Plus


    • Average tire failures: (7.5 + 6.8 + 8.3) / 3 = 7.53
    • Average tire age: (7.1 + 9 + 7.5) / 3 = 7.87
  • Pro Elite


    • Average tire failures: (6.5 + 6.8 + 6 + 6.9 + 5.2) / 5 = 6.28
    • Average tire age: (8.1 + 8 + 6.2 + 6 + 4.5) / 5 = 6.56
The highest average failures per 1000 landings:


  • Grizzly Plus: 7.53
The highest average tire age:


  • Grizzly Plus: 7.87
Conclusion: Yes, the statement is true.

Final Answers


  1. Yes
  2. No
  3. Yes
Is this incorrect for Q3 ?
 
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Hi KarishmaB MartyMurray chetan2u Bismuth83

I am not sure why answer to the part-3 is "No", my reasoning is "Grizzy Plus" satisfies the criteria given in the part-3 question.

Do we care about number of tyres bought by a customer because we are just an average age which is not like the tire failure per 1000 landings? Is this why number of tyres bought by reporting lines matter here?

Could you please explain if I am missing something important here?
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Hi KarishmaB MartyMurray chetan2u Bismuth83

I am not sure why answer to the part-3 is "No", my reasoning is "Grizzy Plus" satisfies the criteria given in the part-3 question.

Do we care about number of tyres bought by a customer because we are just an average age which is not like the tire failure per 1000 landings? Is this why number of tyres bought by reporting lines matter here?

Could you please explain if I am missing something important here?

What is the average age of Grizzly tires? I know it is between 7.1 and 9 but I don't know what exactly it is. That depends on how many tires each airline uses. This is weighted averages and I don't know the weights (the number of tires of each age).
The avg age of Future is between 6.4 and 7.8 and that for Pro Elite is between 6 and 8.1.
It is possible that Grizzly has an avg age of 7.5 and Future or Pro Elite has of 7.6.
So I don't have sufficient info.
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Thanks KarishmaB

I wanted two cents from you, when I did this question, it didn't strike my mind on part-3 trap despite my crystal clear understanding on weighted average. How can I avoid this kind of mistake going forward on similar questions? Does this usually happen with aspirants on hard questions like this? I noticed that I have been doing silly mistakes on 705-805 Graphs & Tables questions which are not due to conceptual gap.

KarishmaB
agrasan
Hi KarishmaB MartyMurray chetan2u Bismuth83

I am not sure why answer to the part-3 is "No", my reasoning is "Grizzy Plus" satisfies the criteria given in the part-3 question.

Do we care about number of tyres bought by a customer because we are just an average age which is not like the tire failure per 1000 landings? Is this why number of tyres bought by reporting lines matter here?

Could you please explain if I am missing something important here?

What is the average age of Grizzly tires? I know it is between 7.1 and 9 but I don't know what exactly it is. That depends on how many tires each airline uses. This is weighted averages and I don't know the weights (the number of tires of each age).
The avg age of Future is between 6.4 and 7.8 and that for Pro Elite is between 6 and 8.1.
It is possible that Grizzly has an avg age of 7.5 and Future or Pro Elite has of 7.6.
So I don't have sufficient info.
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thanks Harvey now it seems clear: I took Mystic avg 9 as the highest, thinking the values are already given in averages but these are for airlines and not for the tire brands.
However the approach must be to estimate/calculate avg age for each tire brands , which for certain max is Grizzly.
Harvey_15_12
­The tire brand with the highest average failures per 1000 landings acMross all reporting airlines also had the highest average tire age across all reporting airlines."

Calculate the average tire failures and tire age for each brand:


  • Future


    • Average tire failures: (6.3 + 5.9) / 2 = 6.1
    • Average tire age: (6.4 + 7.8) / 2 = 7.1
  • Grizzly Plus


    • Average tire failures: (7.5 + 6.8 + 8.3) / 3 = 7.53
    • Average tire age: (7.1 + 9 + 7.5) / 3 = 7.87
  • Pro Elite


    • Average tire failures: (6.5 + 6.8 + 6 + 6.9 + 5.2) / 5 = 6.28
    • Average tire age: (8.1 + 8 + 6.2 + 6 + 4.5) / 5 = 6.56
The highest average failures per 1000 landings:


  • Grizzly Plus: 7.53
The highest average tire age:


  • Grizzly Plus: 7.87
Conclusion: Yes, the statement is true.

Final Answers


  1. Yes
  2. No
  3. Yes
Is this incorrect for Q3 ?
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KarishmaB Bunuel how is the first answer i.e Median = Hero for Tire Failures per 1000?

Say if the data set is {1,2,4,4} the median = 3 right?

Here why are we only taking set as {1,2,4}, I mean only specific values?
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Aabhash777
KarishmaB Bunuel how is the first answer i.e Median = Hero for Tire Failures per 1000?

Say if the data set is {1,2,4,4} the median = 3 right?

Here why are we only taking set as {1,2,4}, I mean only specific values?

Sort as per brand. There are 5 airlines using Pro Elite. The values for tire failures for them are 5.2, 6, 6.5, 6.8 and 6.9 in ascending order.
The median will be the 3rd value i.e. 6.5 which belongs to Hero.
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