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­At a certain university, there is a strong positive correlation betwe

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Abhivas
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­At a certain university, there is a strong positive correlation betwe [#permalink] ­At a certain university, there is a strong positive correlation betwe   13 Feb 2024, 23:04
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­At a certain university, there is a strong positive correlation between the time of day at which university classes are offered and the classes' average (arithmetic mean) grades, with earlier times associated with lower grades. However, for the classes offered at the earliest time but not for any other classes, there was a strong negative correlation between the grades of students in those classes and the number of scheduled classes they missed. In fact, when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time more often than not had significantly higher average grades than classes offered at any other time.Consider the following statement:

At the university in question, classes offered at earlier times ____1____ lower average grades than classes offered later in the day, but when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time ____2____ higher average grades than classes offered later in the day.­
1 2
tended to have
tended not to have
almost always had
seldom, if ever, had
possibly had
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1: tended to have 2: tended to have
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Abhivas
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Re: ­At a certain university, there is a strong positive correlation betwe [#permalink] ­At a certain university, there is a strong positive correlation betwe   13 Feb 2024, 23:09
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chetan2u GMATNinja
Sir,
Please explain the solution.
As per the ChatGpt, The soultions are for (1) tended to have (2) almost always had.
Even I have chosen the similar solutions.
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­At a certain university, there is a strong positive correlation betwe [#permalink] ­At a certain university, there is a strong positive correlation betwe   14 Feb 2024, 00:28
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Abhivas

The solution depends on the strength of a likelihood of an event happening.

As can be seen, in both the blanks we are expected to fit in positive scenario or affirmative case.

So the options conveying negative meaning can be discarded. ‘Seldom, if ever, had’ and ‘tend not to have’ can be discarded.

Let us check the remaining options now.
A. tend to have: regularly behave/act in a particular way. So a general way that could be seen majority of time.
B. Almost always had: This is a very strong relationship. If I were to give a number I would say we talk of a thing happening at least 95% times.
C. Possibly had: The range of event happening could start as low as 10%. Maybe a slight chance.

Now the blanks that have to be replaced. 
Blank 1. Words should replace ‘strong positive correlation’. Now this would mean in most of the cases but is not extreme as shown by words ‘almost always had’. Only possibility - tend to have
Blank 2. Words should replace ‘more often than not’ and ‘strong negative correlation’. Again this would mean in most of the cases. Just tells us that the trend is in a particular way but not as extreme as the words ‘almost always had’. Only possibility - tend to have

My views purely on logical aspect.
I am sure GMATNinja would pitch in with verbal aspects. 
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Re: ­At a certain university, there is a strong positive correlation betwe [#permalink] ­At a certain university, there is a strong positive correlation betwe   14 Feb 2024, 09:54
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At a certain university, there is a strong positive correlation between the time of day at which university classes are offered and the classes' average (arithmetic mean) grades, with earlier times associated with lower grades.
  • Strong positive correlation between
    • the time of the class during the day
    • the average grade of the class
  • Earlier times are associated with lower grades. Thus, later times are associated with higher grades.
  • Let’s say the university has classes at 8 AM, 9 AM, 10 AM, 11 AM, and 12 PM.
  • The statement says that the average grades of classes starting at 8 AM are generally lower than those of classes starting at 9 AM, the average grades of classes starting at 9 AM are generally lower than those of classes starting at 10 AM, and so on.
  • If we pick a class that starts at 9 AM and a class that starts at 10 AM, can we be sure that the first one will have a lower average grade than the latter class?
  • The answer is No. A strong positive correlation does not mean that every data point will follow the same relationship. Some data points may be off. We can expect an overall trend, but we cannot be sure about any two given classes.

However, for the classes offered at the earliest time but not for any other classes, there was a strong negative correlation between the grades of students in those classes and the number of scheduled classes they missed.
  • If we stick with our above example of class timings, this statement says that for classes offered at 8 AM, a strong negative correlation between
    • the grade of a student
    • the number of scheduled classes he or she missed
  • Thus, a student in such a class who has missed one scheduled class is expected to have a better grade than a student in that class who has missed two scheduled classes. Similarly, a student who has missed two scheduled classes is expected to have a better grade than one who missed three scheduled classes. And so on.
  • What about classes offered at times other than 8 AM?
  • We’re specifically told that for such classes, there was NOT a strong negative correlation between the grade of a student and the number of classes he or she missed.
  • If not a strong negative correlation, what relationship existed between these two in those classes?
  • We don’t know. There could be a small negative correlation. Or there could be no correlation. Or there could be a positive correlation. (By the way, a positive correlation will be funny because this would mean that the more classes a student misses, the better his or her grade.)

In fact, when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time more often than not had significantly higher average grades than classes offered at any other time.
  • Given the previous statement, would the grades of those who miss at least 5 classes be lower than the grades of those who miss at most 4 classes?
  • Yes.
  • So, this statement is about excluding those lower-grade students from the class. When we do so, classes offered at 8 AM generally had much higher grades than classes offered at other times.

Consider the following statement:

At the university in question, classes offered at earlier times [b]1[/b] lower average grades than classes offered later in the day,

We’re given in the passage, “earlier times associated with lower grades.” Thus, “generally had” is a good fit for blank 1.

but when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time [b]2[/b] higher average grades than classes offered later in the day.­

Using the last statement of the passage, “more often than not had” fits perfectly in the second blank.

Given this understanding, “tended to have” fits both the blanks. (tend means a tendency, which means more likely than not)

“tended not to have” has the opposite direction.

“almost always had” is incorrect since neither “strong positive correlation” nor “more often than not” means this. (almost always means almost 100%, whereas “tended to have” means greater than 50%)

“seldom, if ever, had” has the opposite direction.

“possibly had” is incorrect since neither “strong positive correlation” nor “more often than not” means this. (possibly means more than 0% chance)­­­
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Re: ­At a certain university, there is a strong positive correlation betwe [#permalink] ­At a certain university, there is a strong positive correlation betwe   22 Mar 2024, 02:05
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Abhivas wrote:
­At a certain university, there is a strong positive correlation between the time of day at which university classes are offered and the classes' average (arithmetic mean) grades, with earlier times associated with lower grades. However, for the classes offered at the earliest time but not for any other classes, there was a strong negative correlation between the grades of students in those classes and the number of scheduled classes they missed. In fact, when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time more often than not had significantly higher average grades than classes offered at any other time.Consider the following statement:

At the university in question, classes offered at earlier times ____1____ lower average grades than classes offered later in the day, but when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time ____2____ higher average grades than classes offered later in the day.­
 

there is a strong positive correlation between the time of day at which university classes are offered and the classes' average (arithmetic mean) grades, with earlier times associated with lower grades.

So classes offered at earlier times have a strong positive correlation, say correlation coefficient is from 0.6 to 0.8. Hence earlier times will often be associated with lower average but certainly not always. 
So of the options, "tended to have" works best. It indicates a "more often that not" tendency. "Almost always had" indicates a correlation coefficient of say 0.98 - a very very strong correlation. 
ANSWER 1. tended to have­


In fact, when the grades of students who missed at least 5 scheduled classes were excluded, classes offered at the earliest time more often than not had significantly higher average grades than classes offered at any other time.

We need to look some something that is equivalent to "more often than not". As discussed previously, this will again be "tended to have".
ANSWER 2. tended to have 

I have discussed correlation in my content. You can read about it on Sunday through the Super Sundays program (details below in my signature) or by clicking on this link: 
https://youtu.be/gN_vlDpUflo
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Re: ­At a certain university, there is a strong positive correlation betwe [#permalink]
22 Mar 2024, 02:05
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