Math 105 - Midterm 1 Study Guide

Vocabulary flashcards covering statistical sampling methods, measures of central tendency and variation, study designs, resistance to outliers, and data visual analysis for Math 105 Midterm 1.

Stratified Sampling

A sampling method in which the population is divided into subgroups (such as drivers under 30 years of age and drivers over 30 years of age) and samples are selected from each subgroup.

Median

The data value that lies in the middle of a dataset when the observations are arranged in ascending order.

Left-Skewed Distribution Relationship

In distributions that are skewed left, the mean is strictly less than the median ($\text{mean} < \text{median}$).

Parameter

A numerical measurement describing a characteristic of an entire population, such as inspecting all $55{,}000\,\text{kg}$ of meat at Wurst Sausage Company and finding $45{,}000\,\text{kg}$ spoiled.

Statistic

A numerical measurement describing a characteristic of a sample, such as finding that $45\%$ of $100{,}000$ randomly selected adults drink at least $48\,\text{oz}$ of water daily.

Measures of Variation

Statistical measurements used to quantify the spread or dispersion of data, which include Range, Interquartile Range (IQR), and Standard Deviation.

Experiment

A study where researchers actively apply a treatment or intervention (such as giving a drug to one group and a placebo to another) to observe the effect on subjects.

Observational Study

A study where characteristics are observed and measured without manipulating conditions or applying treatments, such as measuring pollution levels in a sample of fish from a lake.

Sensitive Statistic

A summary statistic, such as the mean, that is significantly affected by the presence of extreme values or outliers.

Resistant Statistic

A summary statistic, such as the median or Interquartile Range (IQR), that is not significantly affected by extreme values or outliers.

Observational Units

The individual entities or objects from which data values are collected, such as individual penguins in the Penguins dataset.

Footwear Data Median Interval

For the footwear histogram of $N = 40$ statistics students, the median value falls in the interval $10\text{--}20$.

Resistance to Outliers in Summary Statistics

Resistant statistics (median, IQR) remain relatively stable despite extreme observations, whereas sensitive statistics (mean, standard deviation) are significantly altered by outliers.