Businesses, governments, reporters, and ordinary people rely on statistics to understand complicated information. Statistics is a branch of mathematics. It involves gathering information, summarizing it, and deciding what it means. The numbers that result from that work are also called statistics. They can help to predict such things as the weather and how sports teams will perform. They can also describe specific things about large groups of people—for example, the reading level of students, the opinions of voters, or the health of a city's residents.

Collecting data

Statisticians, the people who gather statistics, collect pieces of information, or data, in three basic ways. They refer to trustworthy sources, such as newspapers and reports from reliable organizations. They perform scientific experiments. They also conduct surveys, or ask people questions.

Statisticians must make sure that the data they gather are accurate. If not, their conclusions may be wrong. For example, the questions used in a survey must not influence the answers. Compare these two survey questions:

Sometimes statisticians cannot gather data about every member of a group, often because the group is too large. In such cases they study only part of the group, called a sample. A sample must be carefully chosen. It must accurately represent the larger population. Small samples can provide good data, but larger samples are generally better.

Imagine that the government wants to know the reading level of fourth-grade students in the United States. It would be difficult to measure every single student, so statisticians choose a sample of several hundred students. If out of all fourth graders, 60 percent are girls, then 60 percent of the sample must also be girls. The sample should also have the same proportion of minority students as the whole population of fourth graders.

Summarizing data

Once statisticians have collected their information, they summarize it. They often put the data in graphs or charts, which are easier to read than long lists of data. (See also graph and chart.)

Statisticians also summarize data by calculating numbers called averages. Many people use averages. Weather forecasters use averages to know how much rain or snow usually falls in a certain month. Sports fans use them to tell how often a baseball player gets a hit or a football quarterback completes a pass. Families use them to find out how much houses cost in their town.

There are three kinds of averages. The most common kind is the mean. If health officials want to know the mean weight of adults in a town, they add together all the weights of a sample of people. They then take that sum and divide it by the number of people in the sample. For example, if 100 people weigh a total of 1,500 pounds, then the mean weight is 1,500 pounds divided by 100, or 150 pounds.

The second kind of average is the mode. The mode is simply the number that occurs most often in a sample. If the most common weight in the town's sample is 139 pounds, then the mode is 139. Modes are the only kind of average that can describe information not made up of numbers—for example, letter grades.

The third kind of average is the median, which is the number right in the middle of the sample. If half the sample weighs more than 145 pounds and half the sample weighs less than 145 pounds, then the median weight is 145 pounds. Medians are helpful when there are some unusually high or low numbers in the sample.

Using statistics

Once the data are summarized, people interpret them, or decide what they mean. Newspaper articles, books, and political speeches often include statistics. People use them to support their opinions and to try to convince others to do things. Because statistics are represented by charts, graphs, and numbers, people tend to believe them. However, people can use statistics to twist the truth. It is important to know whether the statisticians collected the data carefully and summarized them accurately.