Organizing and Graphing Data: A Guide

For a handy guide on organizing and graphing data, here is a handy reference guide with some definitions and examples for math students. This is also great for homework for school-aged children.

The average of a group of numbers tells something about the main trend of the data. The three most important kinds of averages are called mode, median, and mean. The range is the difference between the highest and lowest number in a group of numbers.

The mode is the number in the data that occurs most often. If the data do not have a number that appears more than once, there is no mode. A group of numbers can also have more than one mode.

The median is another kind of average. When ordering a list of numbers from least to greatest, the median is the number that falls in the middle. If there is an even number of numbers, there will be two numbers in the middle. To find the median, add the two middle numbers and divide the sum by 2.

The most common average is the mean. the find the mean, add all the numbers in the list, then divide the sum by the total number of addends. The mean may or may not be a number in the list. It may also be different from the median and/or the mode.

Organizing data into tables makes it easier to compare numbers at a glance. Tables can be arranged several ways and still be easy to read and understand.

A bar graph is another way to organize information and data. The height or length of the bars show how much. The higher or longer the bar, the more there is of something. To compare money spent on groceries, comparing two families, you would use a bar graph.

A picture graph is similar to a bar graph. The picture graph uses a picture to represent a certain amount. For example, on a picture graph for Favorite Pizza Toppings, one pepperoni piece may be used to show two votes from the class.. Half a picture means half the number. Picture graphs are often used in newspapers and textbooks.

Circle graphs are a kind of graph that are useful for showing how something is divided into parts. To show how your money is divided into categories, such as housing, vehicles, and utilities, a circle graph would work best.

Line graphs make it easy to see change when comparing something; for instance, rainfall for the year, month by month. Using a line graph, you can estimate which month gets the most rain and what the average rainfall is for your town, for example.

Multiple line graphs are used to make it easy to see change and to compare numbers. These graphs are used to graph sales by month and by item. A key is used to show what each line represents.

Integers are positive or negative whole numbers or zero. Negative integers are numbers less than zero. The opposite of any number is found the same distance from 0 on a number line. The opposite of 6 is -6. When ordering integers, compare two numbers at a time.

To add and subtract integers, use a number line. To add positive integers, move to the right. To add negative integers, move to the left. To subtract integers, change the subtraction problem to an addition problem. Then, change the second number in the problem to its opposite. For example: 2-4 = 2+ (-4) = -2.

To multiply integers multiply the numbers ignoring any negative signs. If the two factors have the same sign, the product is positive. If two factors have different signs, the product is negative. With three or more factors, multiply two numbers at a time and keep track of the signs.

The properties of multiplication are: Any number times 0 equals 0. Any number times 1 equals the number. The order of the factors does not change the product. The grouping of the factors does not change the product..

The rules for dividing integers are the same as for multiplying integers.

To solve a problem with several operations, follow this rule: My Dear Aunt Sally

Multiplication/Division

Addition/Subtraction

First do multiplication and division, in order from left to right and then do all addition and subtraction in order from left to right. These are called the Order of Operations.

Notebook Math Fact Book