STT 231 EXAM 1 QUESTIONS WITH VERIFIED SOLUTIONS LATEST UPDATE 2026

STT 231 EXAM 1 QUESTIONS WITH VERIFIED SOLUTIONS LATEST UPDATE 2026 Variable - Answers any characteristic (or value) recorded for each case. Categorical Variable - Answers identify a case as a measure of a group, placing each case into exactly one of two or more groups. Quantitative Variable - Answers Measure a numerical quantity. Numerical operations like adding and averaging make sense for quantitative variables. MSU students year - Answers Categorical How many credits an MSU Student has earned - Answers Quantitative Discrete variable (Quantitative) - Answers Limited values in a variable domain (can count) Continuous variable (quantitative) - Answers any value in a variable domain (cannot count) Nominal (Categorical) - Answers sort cases into groups that do not have logical arrangements Ordinal (Categorical) - Answers describe variables whose groups have some logical arrangements. Categorical rule - Answers categorical variable with 2 groups MUST be nominal Age (Patients Age in years) - Answers Quantitative Continuous Smoke (Does the patient smoke yes/no) - Answers Categorical Nominal (remember the rule) Quetelet (Weight/(height^2) in (lbs/in^2)) - Answers Numerical Continuous Vitamins (1 = Regularly, 2 = Occasionally, 3 = No) - Answers Categorical Ordinal Whether or not you were born in Michigan - Answers Categorical Nominal Day of the week you were born - Answers Categorical Nominal/Ordinal How many miles you currently are from where you were born - Answers Quantitative Continuous (you can have half miles, 0.75 miles, etc.) Number of prescriptions a patient is taking - Answers Quantitative Discrete (can only be taking 1 or 3 or so, not half) Statistical Distributions - Answers The pattern of a variable over repeated observations (cases) Key Attributes of numerical distributions - Answers Central Tendency, Variability, Shape, Modality, Outliers, Granularity Variability - Answers Describing the spread of dispersion of the data from the center Shape - Answers Describing the skewness or symmetry of the data (Symmetric, Left Skewed, Right Skewed) Modality - Answers Indicating whether the data fall into natural subgroups (how many peaks the data has) Unimodal - Answers 1 peak Bimodal - Answers 2 peaks Multimodal - Answers multiple peaks Set A Variability - Answers Only vary slight from the central tendency Set B Variability - Answers Increased variation from central tendency What type of Skew does this exhibit? - Answers Right Skew, the tail is to the right What type of skew does this exhibit? - Answers Left Skew, the tail is to the left What type of skew does this exhibit - Answers Symmetrical What type of Modality is this? - Answers Bimodal (two peaks) Central Tendency - Answers Describes the balancing point of the data or a typical value the variable described would take on Outliers - Answers individual observations that differ markedly from the pattern established by other observational units. Granularity - Answers where values only at fixed intervals (measuring data every 5 minutes, 1 minute, 2 minutes) Mean - Answers The number that represents the numerical average value. Median - Answers The number which divides the data in half. Half of the measurements are smaller than the median, half are larger. Density - Answers (# of observations)/(length of interval) Do the mean and median have to be identical? - Answers No they do not have to be identical Resistant - Answers Median and IQR (is resistant or not affected by extreme observations) Sensitive - Answers Mean, Range, Standard Deviation (affected by a single extreme observation) Symmetric data - Answers mean = median Right Skewed Data - Answers mean is larger, median stays the same (meanmedian) Left Skewed data - Answers mean is smaller, median stays the same (meanmedian) What follows the tail of data? - Answers Mean Range - Answers 100th percentile - 0th percentile (maximum - minimum) IQR - Answers 75th percentile - 25th percentile (Q3-Q1) Proportion - Answers special case of the mean applied to a simple categorical variable. The categorical variable is deemed 1 = success or 0 = failures. Often expressed as rates or proportions Proportion Formula (pi^ or pi hat) - Answers (Number of success)/(Total number of cases) standard deviation - Answers approximate average distance of the observational units from their common mean value Standard Deviation Formula - Answers S = √(sum of squared deviations from the mean)/(number of cases - 1)