Statistics Terms

Data and sampling 7

• Categorical DataCategorical data are data that sort people or things into groups, or categories, such as eye color, favorite sport or a yes/no answer. The values are labels, not measurements, so you count how many fall in each category and show the counts with a bar graph, a pie chart or a two way table.Grade 6, Grade 8, Algebra 1
• DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Grade 2, Grade 3, Grade 6
• PopulationA population in statistics is the whole group of people, animals or objects you want to learn about, such as every student in a school or every bulb a factory makes. Measuring all of them is often too costly, so you study a sample, a part of the population, and use it to draw conclusions about the whole group.Grade 7, Statistics, Algebra 1
• Relative FrequencyRelative frequency is how often a value or event occurs compared with the total number of observations: frequency ÷ total. It can be a fraction, a decimal or a percent. If 12 of 40 students choose apples, the relative frequency of apples is 12/40 = 0.3, or 30%. All the relative frequencies in a table add to 1.Grade 7, Grade 8, Statistics
• SampleA sample in statistics is a part of a population that is actually observed or measured, such as 60 students surveyed out of a school of 900. You use the sample to estimate facts about the whole population. A random sample, where every member has the same chance to be chosen, tends to represent the population fairly.Grade 7, Statistics, Algebra 1
• Sampling BiasSampling bias happens when the way a sample is chosen makes some members of the population more likely to be picked than others, so the sample does not represent the population. Its results lean the same wrong way every time. Surveying only gym-goers about exercise, or counting only volunteers who reply, are classic examples.Grade 7, Algebra 1, Statistics
• StatisticsStatistics is the branch of math that collects, organizes, analyzes and interprets data to answer questions. Descriptive statistics summarize data with graphs and numbers such as the mean and median. Inferential statistics use a sample to draw conclusions about a whole population, with a stated amount of uncertainty.Grade 6, Grade 7, Grade 8

Data displays 6

• Bar GraphA bar graph uses bars to compare amounts in different categories. The taller or longer the bar, the larger the value it represents. Each bar stands for one category, such as a favorite sport, and its length is read against a number scale. Bars can be vertical or horizontal, with gaps between them.Grade 3, Grade 4, Grade 5
• Box PlotA box plot displays a data set through five numbers: minimum, first quartile, median, third quartile, and maximum. The box holds the middle half of the data, a line inside it marks the median, and whiskers reach out to the smallest and largest values. It makes spread easy to compare between sets.Grade 6, Grade 7, Grade 8
• Dot PlotA dot plot is a graph that shows each data value as a dot above its place on a number line. Dots for repeated values stack up in a column, so the tallest stack shows the mode, and you can see the center, spread, gaps and outliers of the data at a glance.Grade 3, Grade 4, Grade 5
• HistogramA histogram uses bars to show how numerical data are grouped into intervals. The data are split into equal-width intervals, called bins, and each bar's height is the count of values in that interval. The bars touch, because the intervals are continuous, which is what distinguishes a histogram from a bar graph.Grade 6, Grade 7, Grade 8
• Line PlotA line plot shows data values along a number line, often with marks above each value. Each X or dot stands for one data value, and repeated values stack in a column, so the tallest stack is the mode. Line plots make it easy to see clusters, gaps, outliers and the spread of a small data set.Grade 3, Grade 4, Grade 5
• Tally MarkA tally mark is a short line drawn to record one item as you count. Marks are grouped in fives: four vertical lines with a fifth line drawn across them, so a group is easy to see and count by 5s. Tally marks are used to collect data quickly, as in a tally chart of votes.Kindergarten, Grade 1, Grade 2

Measures of center 5

• AverageAn average is one number that stands for the typical size of the values in a data set. In everyday math, average means the mean: add all the values, then divide by how many values there are. In statistics, the median and the mode are also kinds of average.Grade 5, Grade 6, Grade 7
• MeanThe mean is the sum of the values divided by the number of values. It is the arithmetic average: add every value and divide by how many there are. For 3, 7, 5 and 9, the mean is 24 ÷ 4 = 6. The mean is the balance point of the data, so one outlier can pull it far.Grade 5, Grade 6, Grade 7
• MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Grade 5, Grade 6, Grade 7
• ModeThe mode is the value that appears most often in a data set. To find it, count how many times each value occurs and pick the most frequent one. A data set can have one mode, more than one mode, or no mode at all when every value appears only once. The mode works for categories, too.Grade 5, Grade 6, Grade 7
• Weighted AverageA weighted average is an average in which some values count more than others. Multiply each value by its weight, add those products, and divide by the sum of the weights. Course grades, GPAs and combined groups use it, because a plain mean would treat every value as equally important.Grade 7, Grade 8, Algebra 1

Spread and position 8

• Interquartile RangeThe interquartile range (IQR) is the spread of the middle half of a data set: the third quartile minus the first quartile, IQR = Q3 − Q1. Because it ignores the lowest and highest quarters of the data, outliers barely change it. In a box plot it is the length of the box.Grade 6, Grade 7, Algebra 1
• Mean Absolute DeviationThe mean absolute deviation (MAD) is the average distance between each data value and the mean. Find the mean, find how far each value is from it, then average those distances. A small MAD means the data cluster close to the mean; a large MAD means they are spread out.Grade 6, Grade 7
• OutlierAn outlier is a data value that is far away from most of the other values in a set. In 4, 5, 6, 7, 50, the value 50 is an outlier. A common test flags any value more than 1.5 times the interquartile range below the first quartile or above the third. Outliers pull the mean strongly.Grade 6, Grade 7, Grade 8
• PercentileA percentile tells what percent of the values in a data set are at or below a given value. If your test score is at the 80th percentile, about 80% of the scores are at or below yours. The 25th, 50th and 75th percentiles are the first quartile, the median and the third quartile.Grade 7, Algebra 1, Statistics
• QuartileA quartile is one of three values that split an ordered data set into four parts with about the same number of values. The first quartile, Q1, is the median of the lower half; Q2 is the median of all the data; Q3 is the median of the upper half. The interquartile range is Q3 − Q1.Grade 6, Grade 7, Statistics
• RangeThe range of a data set is the difference between the greatest and least values: maximum minus minimum. For 2, 5, 9, the range is 9 − 2 = 7. Range is a simple measure of spread: it tells how far apart the extreme values are, though one outlier can make it misleading about the rest of the data.Grade 5, Grade 6, Grade 7
• Standard DeviationStandard deviation is a number that measures how spread out data values are from their mean: roughly, the typical distance of a value from the mean. A small standard deviation means the values cluster near the mean; a large one means they are spread out. It is the square root of the variance.Algebra 1, Statistics
• VarianceVariance is a measure of spread: the average of the squared distances of the data values from their mean. Find each value's distance from the mean, square it, add the squares, and divide by n for a population (or n − 1 for a sample). Larger variance means more spread. Its square root is the standard deviation.Algebra 1, Statistics

Two-variable data 7

• CausationCausation means a change in one variable directly produces a change in another: the first is the cause and the second is the effect. Two variables can be correlated without causation, because a lurking variable or chance may link them. A well-designed randomized experiment is the standard way to show causation.Grade 8, Algebra 1, Statistics
• CorrelationCorrelation is a measure of how strongly two variables move together in a straight-line pattern. In a positive correlation both rise together; in a negative correlation one rises as the other falls. The correlation coefficient r runs from −1 to 1: values near ± 1 are strong and values near 0 are weak. Correlation does not prove causation.Grade 8, Algebra 1, Statistics
• Correlation CoefficientThe correlation coefficient, r, is a number from −1 to 1 that measures how closely the points of a scatter plot follow a straight line. The sign gives the direction (positive slopes up, negative slopes down), and the size gives the strength: near ± 1 is strong, near 0 is weak or none.Algebra 1, Statistics
• Joint FrequencyJoint frequency is the number of data values that fit two categories at the same time, such as students who are in Grade 7 and play an instrument. In a two-way table, a joint frequency is one of the inside cells, not the totals. Dividing it by the grand total gives the joint relative frequency.Grade 8, Algebra 1
• Line of Best FitA line of best fit is a straight line drawn through a scatter plot that shows the overall trend of the data as closely as possible. It passes through the middle of the points, with about as many above it as below. Its equation, y hat = mx + b, lets you predict one variable from the other.Grade 8, Algebra 1, Statistics
• Scatter PlotA scatter plot displays paired numerical data as points on a coordinate plane, one point for each pair. It helps show whether two quantities have a pattern or relationship: points rising from left to right show a positive association, points falling show a negative association, and a shapeless cloud shows no association.Grade 8, Algebra 1
• Two-Way TableA two-way table shows counts for two categorical variables collected from the same group, with one variable in the rows and the other in the columns. Each inside cell is a joint frequency, and the totals in the margins are marginal frequencies. Dividing a cell by a row or column total gives relative frequencies that reveal associations.Grade 8, Algebra 1

Distributions 3

• Empirical RuleThe empirical rule says that in a bell-shaped (normal) distribution about 68% of the data fall within 1 standard deviation of the mean, about 95% within 2, and about 99.7% within 3. It is also called the 68-95-99.7 rule, and it only works for data that are roughly symmetric and bell-shaped.Algebra 2, Statistics
• Normal DistributionA normal distribution is a symmetric, bell-shaped distribution of data centered at the mean, where the mean, median and mode are equal. Its spread is set by the standard deviation σ. About 68% of values lie within 1σ of the mean, 95% within 2σ and 99.7% within 3σ. Heights and test scores are often close to normal.Algebra 2, Statistics
• Z-ScoreA z-score tells how many standard deviations a value is above or below the mean. Find it with z = (x − μ)/σ: subtract the mean, then divide by the standard deviation. A positive z-score is above the mean, a negative one is below, and z = 0 is exactly at the mean.Algebra 2, Statistics

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Updated November 2026·Reviewed by the Effortless Math team