#separator:tab #html:false #tags column:4 Data Facts or measurements that have been collected math-statistics-terms Population The whole group you want to learn about math-statistics-terms Sample A smaller group taken from the population math-statistics-terms Random sample A sample where every member of the population has an equal chance of being chosen math-statistics-terms Bias A systematic error that tilts results in one direction math-statistics-terms Survey A way of collecting data by asking people questions math-statistics-terms Census A survey of every member of the population math-statistics-terms Variable A characteristic that can take different values math-statistics-terms Categorical data Data sorted into groups or names (Eye color) math-statistics-terms Numerical (quantitative) data Data that are numbers you can measure or count math-statistics-terms Discrete data Data that can only take separate values, like counts math-statistics-terms Continuous data Data that can take any value in a range, like height math-statistics-terms Mean Sum of all values divided by how many values math-statistics-terms Median Middle value of ordered data math-statistics-terms Mode Most frequently occurring value math-statistics-terms Range Maximum minus minimum math-statistics-terms Outlier A value far away from the rest of the data math-statistics-terms Quartile One of three values that split ordered data into four equal parts math-statistics-terms Q1 (first quartile) The median of the lower half of the data math-statistics-terms Q3 (third quartile) The median of the upper half of the data math-statistics-terms Interquartile range (IQR) Q3 − Q1 math-statistics-terms Five-number summary Minimum, Q1, median, Q3, maximum math-statistics-terms Outlier rule (1.5 × IQR) Values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are flagged as outliers math-statistics-terms Percentile The value below which a given percent of data fall math-statistics-terms Variance The average squared distance from the mean math-statistics-terms Standard deviation The square root of variance; typical distance from the mean math-statistics-terms Z-score How many standard deviations a value is from the mean: (x − mean)/s math-statistics-terms Frequency How many times a value occurs math-statistics-terms Relative frequency Frequency divided by the total count math-statistics-terms Cumulative frequency A running total of frequencies math-statistics-terms Histogram A bar graph for numerical data grouped into intervals math-statistics-terms Box plot (box-and-whisker) A graph of the five-number summary math-statistics-terms Dot plot A graph with a dot above a number line for each data value math-statistics-terms Stem-and-leaf plot A table that splits each value into a stem and a leaf math-statistics-terms Scatter plot A graph of ordered pairs showing how two variables relate math-statistics-terms Bar graph A graph using separate bars to compare categories math-statistics-terms Pie chart A circle graph that shows parts of a whole math-statistics-terms Line graph A graph that connects points to show change over time math-statistics-terms Symmetric distribution The left and right sides mirror each other math-statistics-terms Skewed right A longer tail on the right; mean is usually greater than median math-statistics-terms Skewed left A longer tail on the left; mean is usually less than median math-statistics-terms Normal distribution A symmetric bell-shaped distribution math-statistics-terms Empirical rule About 68%, 95% and 99.7% of normal data fall within 1, 2 and 3 standard deviations of the mean math-statistics-terms Correlation A measure of the strength and direction of a linear relationship math-statistics-terms Correlation coefficient (r) A number from −1 to 1 measuring linear correlation math-statistics-terms Positive correlation As one variable increases, so does the other math-statistics-terms Negative correlation As one variable increases, the other decreases math-statistics-terms Correlation vs. causation Two things moving together does not prove one causes the other math-statistics-terms Line of best fit A line drawn to match the trend in a scatter plot math-statistics-terms Regression A method for fitting a model to describe how one variable depends on another math-statistics-terms Residual Actual value minus predicted value math-statistics-terms Extrapolation Predicting beyond the range of the data math-statistics-terms Interpolation Predicting between known data points math-statistics-terms Hypothesis test A procedure for deciding whether data support a claim math-statistics-terms Null hypothesis The default claim that nothing special is going on math-statistics-terms P-value The probability of results at least as extreme as observed if the null hypothesis is true math-statistics-terms Confidence interval A range of values likely to contain the true population value math-statistics-terms Margin of error The amount added and subtracted from an estimate to form an interval math-statistics-terms Sampling distribution The distribution of a statistic over many samples math-statistics-terms Central limit theorem Sample means tend toward a normal shape as sample size grows math-statistics-terms Control group The group in an experiment that does not get the treatment math-statistics-terms Random assignment Using chance to place subjects in experiment groups math-statistics-terms Observational study A study that observes without assigning treatments math-statistics-terms Experiment A study where researchers assign treatments math-statistics-terms