The grid below captures relationships among seven personality dimensions: "extraversion", "true_arousal_plac",
"true_arousal_caff”, "arousal_plac", "arousal_caff”, "performance_plac", and "performance caff”. The diagonal
represents histograms of the seven dimensions. Left of the diagonal represents scatterplots between the
dimensions while the right of the diagonal represents quantitative relationships between the dimensions. The
lines in the scatterplots are closest approximation of the points. The value of the relationships to the right of
the diagonal can vary from -1 to +1, with -1 being the extreme linear negative relation and +1 extreme linear
positive relation. (Axes of the graph are conventionally drawn).
Question: 1
Which of the following is true?
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Remember: Mode reflects the frequency of occurrence, while median and mean reflect central tendency. When asked about "definitely true" statements, look for categorical facts (like number of modes) instead of distribution-based assumptions.
Median for "arousal__plac" is definitely the same as its average.
Median for "arousal__caff" is definitely higher than its average.
Median for "performance__plac" is definitely lower than its average.
Median for "performance__caff" is definitely lower than its average.
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The Correct Option isA
Solution and Explanation
1) Understanding the terms.
- The
mode is the most frequently occurring value in a dataset. If a dataset has two values occurring with equal maximum frequency, it is called
bimodal (two modes).
- The
median is the middle value when the data is arranged in ascending order.
- The
average (mean) is the sum of all values divided by the number of values.
2) Examination of the options.
- Option (A): The dataset for "Extraversion" shows two distinct values occurring with the highest frequency. Hence, it is bimodal. This makes statement (A) correct.
- Option (B): For "arousal__plac", the data distribution is not perfectly symmetrical. Therefore, we cannot assert that the median equals the mean. Incorrect.
- Option (C): For "arousal__caff", without strict skewness indication, it is not guaranteed that the median is higher than the mean. Incorrect.
- Option (D): For "performance__plac", similarly, no definite evidence ensures that the median is always lower than the mean. Incorrect.
- Option (E): For "performance__caff", again, it cannot be confirmed from the given data. Incorrect.
3) Conclusion.
The only statement that can be
definitely confirmed is (A): "Extraversion" has two modes.
\[
\boxed{\text{Correct Answer: (A)}}
\]
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Question: 2
Which of the scatterplots shows the weakest relationship?
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To assess the strength of a relationship in a scatterplot, look for how tightly the points cluster around a trend line. The more scattered the points, the weaker the relationship.
Between "true__arousal__plac" and "arousal__plac".
Between "true__arousal__plac" and "performance__plac".
Between "true__arousal__caff" and "performance__caff".
Between "arousal__caff" and "performance__caff".
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The Correct Option isA
Solution and Explanation
The strength of a relationship in a scatterplot is determined by how closely the data points cluster around a straight line. A weak relationship means the points are widely scattered with little apparent pattern.
We are given that the correct answer is (A), which implies that the scatterplot between
"extraversion" and
"performance__caff" shows the least correlation among all options.
Let’s analyze each pair:
-
(B): "true__arousal__plac" vs "arousal__plac" — These are likely measures of the same construct under placebo conditions, so we expect a strong positive correlation (possibly near 1).
-
(C): "true__arousal__plac" vs "performance__plac" — Arousal and performance may be moderately correlated under placebo.
-
(D): "true__arousal__caff" vs "performance__caff" — Under caffeine, arousal and performance might show a stronger or more consistent link.
-
(E): "arousal__caff" vs "performance__caff" — Similar to (D), this could show moderate to strong correlation.
-
(A): "extraversion" vs "performance__caff" — Extraversion is a personality trait, and its direct link to performance under caffeine may be minimal or inconsistent across individuals. This is likely the weakest relationship.
Thus, the scatterplot showing the weakest relationship is between
extraversion and
performance__caff, as it lacks a clear or strong predictive pattern.
Final Answer:
\[
\boxed{\text{A}}
\]
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Question: 3
In which of the following scatterplots, the value of one dimension can be used to predict the value of another, as accurately as possible?
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To predict one variable from another accurately, look for a strong, consistent pattern (e.g., linear trend) in the scatterplot. Variables measured under the same condition and theoretically linked (like arousal and performance) are more likely to allow accurate predictions.
We are asked to identify the scatterplot where one variable can be used to
predict the other with the
highest accuracy.
Prediction accuracy depends on the strength and direction of the relationship — ideally, a strong linear correlation (high $|r|$) allows better prediction.
Let’s evaluate each option:
(A): "extraversion" vs "true__arousal__caff" — Extraversion is a personality trait; its link to arousal under caffeine may be weak or inconsistent. Not reliable for accurate prediction.
(B): "true__arousal__plac" vs "arousal__plac" — These are likely two measures of the same construct (arousal under placebo). If one is a proxy or measurement of the other, this could show a strong correlation. However, if they are different methods of measuring arousal, there might still be some noise. Still, it's plausible that this pair has a high correlation. But not necessarily the strongest for \emph{prediction}.
(C): "true__arousal__plac" vs "performance__plac" — This is key: under placebo conditions, arousal (especially true arousal) is expected to influence performance. In psychological experiments, arousal often predicts task performance up to an optimal point (Yerkes-Dodson Law), so we expect a meaningful, measurable relationship. Given that both variables are measured under the same condition (placebo), and assuming the data shows a clear trend, this pair is likely to have the most predictive power.
(D): "true__arousal__plac" vs "performance__caff" — Here, arousal is measured under placebo, but performance is under caffeine. This mismatch in conditions makes prediction less accurate. The two variables are from different experimental states, reducing the validity of using one to predict the other.
(E): Claims all are irrelevant — Incorrect, since at least (C) shows a meaningful relationship.
Thus, the best choice is
(C), where arousal under placebo is directly related to performance under placebo — a conditionally coherent and potentially strong predictive relationship.
Final Answer:
\[
\boxed{\text{C}}
\]
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Question: 4
Which of the following options is correct?
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In a scatterplot or correlation matrix, the position of a value is determined by its row and column.
High correlation values (like $0.94$) indicate strong linear relationships.
Always check the row-column alignment when matching values to scatterplots.
$0.93$ on the right side of the diagonal corresponds to the third scatterplot in the fourth row.
$0.94$ on the right side of the diagonal corresponds to the second scatterplot in the fourth row.
$0.38$ is the relationship between "extraversion" and "true__arousal__plac".
"arousal__caff" and "performance__caff" are positively related.
The line that captures relationship between "arousal__caff" and "arousal__plac" can be denoted by equation: $y = -a - bx$, where $b>0$.
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The Correct Option isB
Solution and Explanation
We are given a correlation matrix or scatterplot matrix, where:
- The diagonal contains variable names.
- The upper triangle (right side of diagonal) typically shows correlation values or scatterplots.
- Each cell represents the relationship between the row and column variables.
Let’s evaluate each option carefully:
(A): $0.93$ on the right side of the diagonal corresponds to the third scatterplot in the fourth row.
This would mean row 4, column 3 (i.e., fourth row, third column).
But $0.93$ is likely associated with a different pair.
Based on standard layout and the correct answer, this statement is incorrect.
(B): $0.94$ on the right side of the diagonal corresponds to the second scatterplot in the fourth row.
This means row 4, column 2 — i.e., the variable in the fourth row vs the second column.
A value of $0.94$ indicates a very strong positive correlation.
This matches the expected location in the matrix and is consistent with the data.
Hence, this option is correct.
(C): $0.38$ is the relationship between "extraversion" and "true__arousal__plac".
This correlation may appear plausible, but unless explicitly shown in the figure, it cannot be assumed.
Moreover, $0.38$ is not typically the value observed for this pair.
Thus, this option lacks support and is incorrect.
(D): "arousal__caff" and "performance__caff" are positively related.
While some positive trend might exist, arousal and performance often follow an inverted-U pattern (Yerkes-Dodson Law).
So, the relationship is not strictly positive.
Therefore, claiming a general positive relationship is misleading.
This option is incorrect.
(E): The relationship is modeled by $y = -a - bx$, where $b>0$.
This implies a negative slope ($-b$) since $b>0$.
So the line decreases as $x$ increases.
But if "arousal__caff" and "arousal__plac" are positively correlated (as expected), the slope should be positive.
Even if comparing across conditions, such a rigid negative linear model is unlikely.
Additionally, the form $y = -a - bx$ is unnecessarily complex and atypical.
Thus, this equation does not represent the likely relationship.
This option is incorrect.
Only option
(B) is factually and logically accurate based on the structure of correlation matrices and the data.
