Exploring One–Variable Data
When comparing standard deviations from two distinct but related samples where one sample size is significantly larger than another, what inference can be made if their standard deviations are similar?
Larger samples always yield more accurate standard deviations hence any similarity indicates underestimation in small samples' variability measure.
Sample size does not inherently affect standard deviation calculation; similarity suggests comparable population variability despite different sample sizes.
Similarity insinuates that both populations might not actually be distinct given parallel dispersion around each respective mean value point estimator-wise.
The smaller sample must have less intrinsic variability which compensates for estimation errors due to lower N count.
Which of the following provides the best measure of center for a highly skewed distribution with outliers?
Mean
Range
Mode
Median
Given a positively skewed distribution, which measure of spread might give a misleading impression of variability if outliers are present?
Variance
Range
Standard deviation
Interquartile range (IQR)
In measuring heights of students in an AP Statistics class, one student's height is much greater than others'; this student's height could be considered what type of value?
The mode
An error
The median
An outlier
In the context of regression analysis, if the correlation coefficient squared equals what percentage of explained variation in the dependent variable (y) can be attributed to the independent variable (x)?
It signifies the percent of unexplained relationship between the variables.
It represents the explained variation in the independent variable.
It exemplifies the total possible correlation that could exist between the two factors.
It implies that no underlying linear pattern is found linking the elements involved.
What describes IQR or interquartile range?
Mean average of all values outside the range
Total number of all data points in the set
Difference between Q1 quartile and Q3 quartile
Midpoint between Q1 quartile and Q3 quartile
Given five number summary data (minimum, Q1, median , Q3 , maximum) with Q3 being substantially closer to the maximum than Q1 is to minimum , indicates which characteristic in boxplot?
Left-skewed distribution
Uniform-distribution
Right-skewed distribution
Bimodal-distribution

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Which summary statistic could decrease even if additional high-value outliers are added to a right-skewed distribution?
Range
Median
Interquartile Range (IQR)
Mean
What statistical measure indicates how spread out numbers are in your dataset?
Range
Standard deviation
Mode
Median
What statistic could reveal whether two variables have a linear relationship if you're considering two quantitative variables with potential outlier influence?
Chi-squared test statistic
Pearson's correlation coefficient
Scatterplot slope
Spearman's rank correlation coefficient