Stats test review with examples

Statistics

The science of collecting, organizing, analyzing, interpreting, and presenting data. Example: Analyzing survey results to understand customer satisfaction.

Data

Collections of observations or values. Example: A list of test scores from a class.

Population

The entire group being studied. Example: All students in a school.

Sample

A smaller group selected from a population. Example: 50 students chosen from a school.

Parameter

A numerical measurement describing a population. Example: The average height of all students in a school.

Statistic

A numerical measurement describing a sample. Example: The average height of 50 sampled students.

Variable

A characteristic that can change. Example: Age of a person.

Qualitative Data

Categorical data described by labels or words. Example: Eye color (blue, brown, green).

Quantitative Data

Numerical data representing counts or measurements. Example: Number of books owned.

Discrete Data

Countable numerical data, usually whole numbers. Example: Number of siblings.

Continuous Data

Measured numerical data that can include decimals. Example: Height or weight.

Nominal Level

Categories only with no meaningful order. Example: Types of fruit (apple, banana, orange).

Ordinal Level

Categories with a meaningful order. Example: Class rankings (1st, 2nd, 3rd).

Interval Level

Numerical data with equal spacing but no true zero. Example: Temperature in Celsius.

Ratio Level

Numerical data with equal spacing and a true zero. Example: Weight in kilograms.

Observational Study

A study where researchers observe without changing anything. Example: Watching animal behavior in the wild.

Experiment

A study where treatments are applied to observe effects. Example: Testing a new drug on patients.

Convenience Sampling

Sampling people who are easiest to reach. Example: Surveying people at a mall.

Random Sampling

Sampling where everyone has an equal chance of being selected. Example: Drawing names from a hat.

Systematic Sampling

Selecting every kth individual from a population. Example: Choosing every 10th person in a list.

Stratified Sampling

Dividing a population into groups and sampling from each. Example: Sampling students from each grade level.

Cluster Sampling

Dividing a population into clusters and randomly selecting clusters. Example: Selecting entire classrooms randomly.

Bias

A flaw that causes some individuals to be more likely selected than others. Example: Surveying only morning students.

Descriptive Statistics

Methods for organizing and summarizing data. Example: Calculating averages and making charts.

Inferential Statistics

Using sample data to make conclusions about a population. Example: Predicting election results from a poll.

Frequency

The number of times a value occurs. Example: A score of 80 appears 3 times.

Relative Frequency

The proportion or percentage of times a value occurs. Example: 3 out of 10 students scored 80 (30%).

Bar Graph

A graph used for categorical data with separated bars. Example: Comparing favorite colors.

Pie Chart

A circular chart divided into slices representing proportions. Example: Showing budget distribution.

Histogram

A graph for quantitative data where bars touch. Example: Distribution of test scores.

Mean

The average found by adding all values and dividing by the number of values. Example: (2+4+6)/3 = 4.

Median

The middle value in an ordered data set. Example: In 1, 3, 5, the median is 3.

Mode

The most frequently occurring value. Example: In 2, 2, 3, the mode is 2.

Range

The difference between the maximum and minimum values. Example: 10 − 2 = 8.

Standard Deviation

A measure of how far data values tend to be from the mean. Example: A low value means data is close to the average.

Variance

The square of the standard deviation. Example: If SD = 2, variance = 4.

Percentile

A measure indicating the percentage of data below a value. Example: Scoring in the 90th percentile.

Quartiles

Values that divide data into four equal parts. Example: Q1, Q2 (median), Q3.

Interquartile Range (IQR)

The difference between Q3 and Q1. Example: Q3 = 15, Q1 = 5, IQR = 10.

Boxplot

A graph based on the 5-number summary. Example: Showing min, Q1, median, Q3, max.