I29-160

Question

https://gmatclub.com/gmat-focus-tests/resources/import/img/I29-160.png 
 
The graph provides data on weekly reaction times and resulting energy yields from 32 trials carried out by four research labs in the Andean Valley in 2022. Each lab conducted eight trials, and for every trial both the reaction time (in hours) and the resulting energy yield (in kilojoules) were recorded.
 
Select from each drop-down menu the option that creates the most accurate statement based on the information provided.

The range of the recorded energy yields was greatest for Lab  GRAPH_1_PLACEHOLDER .

The median reported reaction time for all trials across the four labs was  GRAPH_2_PLACEHOLDER  the median reported reaction time for all trials across the three labs excluding Lab D.

Bunuel · Answer

Official Solution:

Drop-down 1: 
 
The range of a data set is the maximum value minus the minimum value.
 
From the graph, the lowest yield is 260 and the highest yield is 1400, both from Lab D. Since both extremes belong to Lab D, Lab D has the greatest range.
 
Correct answer:  Lab D 
 
 Drop-down 2: 
 
The median is the middle value of a data set in ascending order, or the average of the two middle values if the total number is even.
 
Across all 32 trials, the median is the average of the 16th and 17th values: (4 + 5)/2 = 4.5.
 
Across the 24 trials excluding Lab D, the median is the average of the 12th and 13th values: (4 + 5)/2 = 4.5.
 
Thus, the two medians are the same.
 
Correct answer:  the same as

Correct answer:

Dropdown 1:  "Lab D"

Dropdown 2:  "the same as"

andy1997 · Answer

I don’t quite agree with the solution. . Median is bigger

Bunuel · Answer

The medians match because of how the values line up when ordered. With all 32 trials, the 16th and 17th values are 4 and 5, so the median is (4 + 5)/2 = 4.5. When Lab D is excluded, there are 24 trials left, and the 12th and 13th values are again 4 and 5, so the median is (4 + 5)/2 = 4.5. That is why the result is the same in both cases.

And as a reminder, when you claim something is larger or smaller, you should show the ordered values or the calculation, not just state it.

P.S. When you make a claim, it’s always better to show how you got it so we can address it directly. Throwing out a statement without backing it up is pointless.

abhikc3004 · Answer

I like the solution - it’s helpful.

confusedchild · Answer

I like the solution - it’s helpful. drop down 1 was very clear. For drop down 2, i'm not sure i understand.

How are we saying that the 16th & 17th value is 4+5/2
and the 12th & 13th value is also 4+5/2?

I do realize that the median reported reaction time is 4+5/2, coz out of the 8 hours those are the the average of 4th & 5th hour is the median hour, right?
But where do 12th, 13th & 16th 17th come from and how are we counting this & equating it to 4+5/2 - i'm unable to understand.

Thanks in advance for the help!

Bunuel · Answer

There are 32 trials total, and  each reaction time from 1 to 8 hours occurs once for each of the 4 labs .

So, when all 32 reaction times are arranged from smallest to largest, they are:

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,     4    ,     5    , 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8

Since there are 32 values, the median is determined by the  16th and 17th values . The 16th value is 4 hours and the 17th is 5 hours, so the median is (4 + 5)/2 = 4.5.

Excluding Lab D, there are 24 trials, with each reaction time appearing 3 times:

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,     4    ,     5    , 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8

Now the middle values are the  12th and 13th . Again, these are 4 and 5, so the median is also 4.5.

So the 16th/17th and 12th/13th come simply from the number of observations in each data set.

I29-160

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