Data 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.
In Spanish
datos
Also called
data set, datum (one value), information, statistics data
The same 12 answers as a list, a table and a bar graph. Organizing data is what turns a jumble of answers into a pattern you can read.
Formal definition and notation
In statistics, data are the observed values of one or more variables for the individuals in a population or sample; a single value is a datum. A numerical (quantitative) variable takes number values with units, such as weight in pounds; a categorical (qualitative) variable places each individual into a group, such as blood type. A collection of values is a data set.
Symbol
Read it as
Meaning
n
n
the number of values in a data set
x1, x2, …, xn
x one, x two, through x n
the individual values of a numerical data set
Key facts
Data can be numbers (numerical or quantitative) or words and labels (categorical or qualitative).
Numbers used as labels, like ZIP codes or jersey numbers, are categorical: averaging them means nothing.
Raw data are first organized, for example in a tally chart or frequency table, then displayed in a graph.
A statistical question expects variability in the data: “How many hours do students in my class sleep?” rather than “How old am I?”
Numerical data can be summarized by a center, such as the mean or median, and a spread, such as the range.
Try it: explore a numerical data set
Interactive
These are the hours of sleep reported by 10 students. Drag a dot to change a value, then watch how the mean, median, mode and range respond.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Data examples, step by step
Example 1: Numerical or categorical?
Warm-up
A class records each student’s shoe size, eye color, number of pets and favorite sport. Which of these are numerical data?
Ask: is it a measurement or a count that you could average?
Shoe size is a measurement and number of pets is a count: numerical.
Eye color and favorite sport are labels: categorical.
Answer: Shoe size and number of pets are numerical; eye color and favorite sport are categorical.
Example 2: Read a frequency table
Core
In a survey of 20 students, 8 chose pizza, 5 chose tacos, 4 chose pasta and 3 chose salad. What percent chose pizza, and how many more chose pizza than salad?
Check the total: 8 + 5 + 4 + 3 = 20.
Percent for pizza: 820 = 0.4 = 40%.
Pizza minus salad: 8 − 3 = 5.
Answer: 40% chose pizza, and 5 more students chose pizza than salad.
Example 3: Summarize numerical data
Test-style
Six plants grew 12, 15, 9, 15, 14 and 13 cm in a month. Find the mean and the median growth.
Data are the collected values themselves. Statistics is the science of collecting, organizing and interpreting data, and a statistic is one number that summarizes a sample, like its mean.
In statistics, a variable is the characteristic being recorded, such as height. The data are the actual values: 142 cm, 150 cm, 138 cm.
Quick check: 3 questions
Question 1 of 3
Which of these is categorical data?
Show answer and explanation
Answer: B. Favorite colors are labels, so they are categorical. Heights, page counts and race times are measured or counted numbers, so they are numerical.
Question 2 of 3
A table shows apple 5, banana 3 and grape 4. How many more students chose apple than banana?
Show answer and explanation
Answer: D.5 − 3 = 2. Choice A adds the two counts, B is the apple count alone, and C compares apple with grape.
Question 3 of 3
Which is a statistical question?
Show answer and explanation
Answer: C. It expects different answers from different students, so it produces data with variability. The other questions each have one fixed answer.
Data: frequently asked questions
Is data singular or plural?
Strictly, data is plural: one value is a datum, and many values are data, so careful writers say the data are. In everyday English people also treat data as a singular mass noun, as in the data is ready, and most teachers accept both. In math and science writing, the plural form is common.
What is the difference between numerical and categorical data?
Numerical data are numbers that measure or count something, like 142 cm or 3 pets, so you can add them and find a mean. Categorical data put each item into a group, like red or blue, so you count how many fall in each group instead. Numbers used as names, like phone numbers, count as categorical.
How do you organize data?
Start by sorting the raw values. For categorical data, make a tally chart or frequency table that counts each category, then draw a bar graph. For numerical data, put the values in order, then use a dot plot, histogram or box plot, and summarize with a center (mean or median) and a spread (range).
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.Statistics · Grade 6, Grade 7, Grade 8PopulationA 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.Statistics · Grade 7, Statistics, Algebra 1SampleA 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.Statistics · Grade 7, Statistics, Algebra 1NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Categorical 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.Statistics · Grade 6, Grade 8, Algebra 1Bar 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.Statistics · Grade 3, Grade 4, Grade 5Dot 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.Statistics · Grade 3, Grade 4, Grade 5HistogramA 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.Statistics · Grade 6, Grade 7, Grade 8Box 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.Statistics · Grade 6, Grade 7, Grade 8MeanThe 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.Statistics · Grade 5, Grade 6, Grade 7MedianThe 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.Statistics · Grade 5, Grade 6, Grade 7RangeThe 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.Statistics · Grade 5, Grade 6, Grade 7AverageAn 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.Statistics · Grade 5, Grade 6, Grade 7VariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6Line 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.Statistics · Grade 3, Grade 4, Grade 5ModeThe 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.Statistics · Grade 5, Grade 6, Grade 7Two-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.Statistics · Grade 8, Algebra 1