WorksheetsPage 1
Total questions: 20
Worksheet time: 10mins
For sample standard deviation, why is N−1 used in the denominator instead of N?
Ensures mean equals median
Eliminates outliers automatically
Gives closer real-world estimate
Simplifies computation steps
Why might N−1 be used instead of N when computing kurtosis numerators?
To match Pearson’s skew index
Bias correction in finite samples
To increase numerical stability
Because σ is unknown always
Given deviations |x − μ| are summed and divided by N, what statistic is obtained?
Mean absolute deviation
Interquartile range
Standard deviation
Coefficient of variation
What is the primary purpose of CV in data analysis?
Transform skewed distributions to normal
Detect outliers in a single dataset
Compare datasets with different units
Estimate the population mean accurately
A Q–Q plot primarily compares what?
Sample means to population means
Dataset medians to interquartile ranges
Sample quantiles to theoretical quantiles
Observed deviations to absolute deviations
When points deviate strongly from the Q–Q plot’s reference line, what is the most appropriate next step?
Conduct careful analysis before interpretation
Immediately assume data are uniformly distributed
Discard outliers and proceed with conclusions
Transform data without checking assumptions
If a scatter plot were drawn from the table, which line type would most likely fit the trend?
A downward-sloping linear fit
A horizontal line through the mean
A sinusoidal curve with multiple peaks
An upward-sloping linear fit
Which statement best describes the primary purpose of a scatter plot in data analysis?
Display bivariate relationships with two variables
Summarize categorical counts by one variable
Show ranked ordering of discrete categories
Visualize hierarchical groupings across levels
Before calculating a correlation coefficient, which plot is useful for exploratory checks of anomalies?
Box plot of grouped categories
Pie chart of categorical segments
Histogram of a single variable
Scatter plot of the two variables
In a system where A is an m×n matrix and y is an n-dimensional vector, how is the term ‘augmentation matrix’ formed during Gaussian elimination?
By stacking A and y rowwise
By multiplying A and y elementwise
By appending y to A columnwise
By appending x to y columnwise
When a linear system has exactly one solution, how is the system classified?
Consistent dependent system
Consistent independent system
Overdetermined inconsistent system
Indeterminate contradictory system
What is the goal of reducing a matrix to reduced echelon form in Gaussian elimination?
To maximize sparsity of A
To compute eigenvectors quickly
To verify orthogonality of rows
To isolate pivot positions for solving
After reaching reduced echelon form, which method retrieves remaining unknowns starting from xn?
LU factorization with partial pivoting
Back-substitution from xn downward
Iterative gradient descent on x
Forward substitution from x1 upward
What does the Probability Density Function (PDF) represent for a continuous variable?
Cumulative probability up to any value
Exact probability at a single point
Frequency counts of discrete events
Shape of distribution via density values
Which function computes the probability of observing a value less than or equal to x?
Likelihood Function (LF)
Probability Mass Function (PMF)
Probability Density Function (PDF)
Cumulative Distribution Function (CDF)
Which statement about machine learning datasets and distributions is accurate?
They do not require sampling theory at all
They may be generated by multiple distributions
They always follow one perfect distribution
They never involve random variables
For the Poisson distribution with parameter λ, what is the standard deviation?
√λ
λ
1/√λ
√(λ/2)
In the course registration table, what is the total number of students?
90
80
100
110
Which conclusion is justified if the computed χ² is below the critical value for df = 1?
Accept significant difference in registration rates
Reject independence between gender and registration
Conclude boys register more than girls definitively
Fail to reject the null hypothesis of independence
Why does PCA lead to a reduced dimension representation?
It removes outliers using robust loss functions
It binarizes continuous features for simplicity
It exploits information redundancies across measurements
It balances class distributions via resampling
