Prob & Stats Unit 1 Review Flashcards

Statistics

the science of collecting, organizing, summarizing,
and analyzing information to draw conclusions or answer questions

Population

The entire group we wish to study or make conclusions about

Parameter

A numerical summary calculated based on data from all individuals in the group of interest; it describes a characteristic of the population.

Sample

A subgroup of the entire group of interest.

Statistic

A numerical summary calculated based on data taken from a sample of the population; it describes a characteristic of the sample.

Qualitative Data

Non-numerical information that describes characteristics or qualities of a population or sample.

Quantitative Data

Numerical information that represents measurements or counts, allowing for mathematical calculations and statistical analysis.

Discrete Data

Quantitative data that can take on a countable number of values; finite; Ex. the number of students in a class or the number of cars in a parking lot.

Continuous Data

Quantitative data that can take on any value within a given range; infinite possibilities; Ex. height, weight, or temperature.

Nominal

a type of categorical data that represents distinct categories without any intrinsic ordering; examples include gender, race, or hair color.

Ordinal

a type of categorical data that represents distinct categories with a meaningful order or ranking, but without consistent intervals between the categories; examples include education level, customer satisfaction ratings, or ranks in a competition.

Ratio

a type of quantitative data that possesses a true zero point, allowing for meaningful comparisons and calculations; examples include weight, height, and duration.

Interval

a type of quantitative data that has consistent intervals between values but no true zero point; examples include temperature in Celsius or Fahrenheit and dates.

Observational Study

A research method in which the researcher observes and records behavior without manipulating any variables. It aims to gather data in a natural setting to understand relationships between variables.

Experimental Study

A research method where the researcher manipulates one or more independent variables to observe their effect on a dependent variable, often using control and experimental groups to establish cause-and-effect relationships.

Cross-Sectional Study

A research method that examines a population at a single point in time, providing a snapshot of data for analysis of relationships and characteristics.

Case-Control Study

A research method comparing subjects with a particular condition to those without, looking back in time to identify potential risk factors.

Cohort Study

A research method that follows a group of individuals over time to assess the development of outcomes, comparing those exposed to a certain factor with those not exposed.

Confounding Variable

A variable that influences both the dependent and independent variable, potentially leading to a false association between the two; considered, but unable to
distinguish from another variable

Lurking Variable

A variable that is not measured or considered in a study but can affect the outcome, potentially leading to misleading conclusions.

Placebo

A substance with no therapeutic effect used as a control in experiments to test the effectiveness of another substance.

Blinding

The practice of keeping study participants unaware of whether they are receiving the treatment or placebo to reduce bias in research results.

Frame

a list of all members of the population; it serves as the basis for selecting samples.

Convenience Sampling

A non-probability sampling technique where samples are selected based on their easy availability and proximity to the researcher, potentially leading to biased results.

Simple Random Sampling

A sampling method where each individual has an equal chance of being chosen from a population, usually achieved through random selection.

Stratified Random Sampling

A sampling method where the population is divided into distinct subgroups, and samples are randomly selected from EACH stratum to ensure representation.

Systematic Random Sampling

A sampling method where individuals are selected from a larger population at regular intervals, often using a RANDOM starting point.

Cluster Random Sampling

A sampling method where the population is divided into groups, usually geographically, and entire groups are randomly selected to be included in the sample; an entire group may be left out of this sampling method.

Multistage Sampling

A sampling method that combines multiple sampling techniques, such as cluster sampling and stratified sampling, to select samples from different stages or levels of the population. This method allows for flexibility and efficiency in obtaining a representative sample from large populations; teacher says most common is cluster → SRS 

Bias

Occurs when results are not representative of reality, potentially due to poor sampling procedures, low response rates, problematic survey questions, faulty analysis, or bad luck that skews the findings and leads to incorrect conclusions.

Non-Response Bias

A type of bias that occurs when individuals selected for a survey or study do not respond, leading to a potential distortion in the overall results if the non-respondents differ significantly from respondents; mitigate through incentives

Response Bias

answers provided on a survey do not reflect the reality of the
respondent’s feelings or beliefs, often due to leading questions, social desirability, or misunderstanding.

Frequency Distribution

A summary of how often each value occurs in a data set, typically displayed in a table or graph to show the distribution of values. It helps to visualize the data's shape, central tendency, and variability.

Relative Frequency

indicates the proportion (or percentage) of observations within that
category; calculated by dividing the frequency of a category by the total number of observations.

Bar Graph

A graphical representation of data using rectangular bars, where the length of each bar is proportional to the value it represents; are commonly used to compare different categories; bars don’t touch

Pareto Chart

A type of bar graph where the values are represented in descending order, highlighting the most significant factors in a dataset; often used for quality control and decision making.

Pie Charts

A circular graph divided into slices, each representing a proportion of the whole; commonly used to show percentage or proportional data. Compares relative frequencies for qualitative data

Histogram

similar to a bar graph, only it is for quantitative data; bars should touch; It visually displays the distribution of numerical data by grouping values into intervals or bins, allowing for identification of patterns such as skewness or modality.

Classes

Intervals that group quantitative data in a histogram, allowing for analysis of the frequency of data points within those ranges.

Lower Class Limit

smallest possible value within a class

Upper Class Limit

largest possible value within a class

Class Width

the difference between consecutive classes’ lower limits; NOT upper limit - lower limit

Stem-and-Leaf Plot

a method of displaying quantitative data that separates the digits of each value into a "stem" and a "leaf."

Dot-Plot

a statistical chart that uses dots to represent the frequency of data points along a number line.

Skew

A type of distribution in which data points are not symmetrically distributed around the mean, resulting in a longer tail on one side.

Skewed Left

A distribution where most values are concentrated on the right side, causing the tail to extend to the left. It indicates that a majority of data points are above the mean.

Skewed Right

A distribution where most values are concentrated on the left side, causing the tail to extend to the right. It indicates that a majority of data points are below the mean.

Time Series Graph

A graphical representation that displays data points over time, showing trends and patterns in the data across chronological intervals.

Central Tendency

A statistical measure that identifies a single score as representative of an entire dataset, commonly using mean, median, or mode to summarize the data; shape, center, and spread

Mean

the average value of a dataset, calculated by dividing the sum of all values by the number of values. It is a measure of central tendency that provides a central point around which the data is distributed; true ‘average,’ non-resistant statistic

Population Mean

the average of a population data set, calculated similarly to the sample mean but includes all members of the population.

Sample Mean

the average calculated from a sample of a population, used to estimate the population mean; obtained by dividing the sum of the sample data by the number of observations in the sample.

Median

the middle value of a dataset when arranged in ascending or descending order; if there is an even number of observations, the median is the average of the two middle numbers. It is another measure of central tendency; resistant statistic

Resistant Statistic

A statistic that is not affected by extreme values or outliers, making it a robust measure of central tendency, such as the median.

Outlier

A data point that significantly differs from other observations in a dataset, which can skew results and affect statistical calculations.

Mode

The value that appears most frequently in a dataset, which can be used as a measure of central tendency.

Dispersion

The extent to which values in a dataset differ from each other and the average; common measures include range, variance, and standard deviation.

Range

The difference between the largest and smallest values in a dataset, providing a measure of how spread out the values are; non-resistant

Standard-Deviation

A measure of the amount of variation or dispersion in a set of values; it quantifies how much the individual data points differ from the mean; non-resistant

Population Standard Deviation

The standard deviation calculated using the entire population data rather than a sample. It provides a precise measure of variability for a whole population. (unadj. std. var.)

Sample Standard Deviation

The standard deviation calculated from a sample of data, used to estimate the variability of the larger population. It adjusts for sample size by applying Bessel's correction. (std. var.)

Variance

the square of the standard deviation; a measure of the dispersion of a set of values, indicating how far each number in the set is from the mean.

Empirical Rule (68-95-99.7 Rule)

A statistical rule that states for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations; non-resistant; ABOUT

Chebyshev’s inequality

The minimum percentage of observations within k standard
deviations of the mean is; A statistical theorem that states for any data distribution, at least 1 - (1/k²) of the data lies within k standard deviations from the mean, where k > 1; resistant; AT LEAST

Z-Score

A statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations. It indicates how many standard deviations a data point is from the mean; mean of 0 and a standard deviation of 1

Percentiles

measures that indicate the value below which a given percentage of observations fall in a dataset; two parts: above and below the value

Quartiles

values that divide a dataset into four equal parts, with each representing 25% of the data; (Q1, Median, Q2)

Interquartile Range (IQR)

A measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset. It effectively shows the middle 50% of data points, helping to identify outliers; resistant

5-Number Summary

A summary that provides five key values of a dataset: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It offers a quick overview of the dataset's distribution.

Box-Plots

A graphical representation of the 5-number summary that displays the distribution of a dataset; show the median, quartiles, and any potential outliers.