Bar and Histograms (What Would You Use: Part 1)
Teacher background

## Bar Graphs

Bar graphs can be used to show how something changes over time or to compare items. They have an x-axis (horizontal) and a y-axis (vertical). Typically, the x-axis has numbers for the time period or what is being measured, and the y-axis has numbers for the amount of stuff being measured. Bar graphs are good when you're plotting data that spans many years (or days, weeks...), has really, big changes from year to year (or day to day...), or when you are comparing things.

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## The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event." The probability of the occurrence of an event can be expressed as a fraction or a decimal from 0 to 1. Events that are unlikely will have a probability near 0, and events that are likely to happen have probabilities near 1.

In any probability problem, it is very important to identify all the different outcomes that could occur. For instance, in the question about the dice, you must figure out all the different ways the dice could land, and all the different ways you could roll a specific number.Continuing with this "dice example" there are many different sums you can get when rolling dice. The sums are {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. However, each of these sums is not equally likely. The only way to get a sum 2 is to roll a 1 on both dice (1-1), but you can get a sum of 4 three different ways (3-1, 2-2, or 1-3). With this in mind, there are six different ways to get a sum of 7 (1-6, 2-5, 3-4, 4-3, 5-2, or 6-1) which means theoretically the bar representing the number 7 should be larger than the other bars as the number of times the dice are rolled increases.

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## Histograms versus Bar Graphs

Histograms resemble bar charts closely. One main difference is that histograms will normally be shown with the bars touching each other, with no spacing in between, to account for the continuous nature of the data, whereas simple bar charts tend to have spaces to separate the bars.

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I think of histograms as "sorting bins." You have one variable, and you sort data by this variable by placing them into "bins." Then you count how many pieces of data are in each bin. The height of the rectangle you draw on top of each bin is proportional to the number of pieces in that bin. The main question a histogram answers is: "How many measurements are there in each of the classes of measurements?" On the other hand, in bar graphs you have several measurements of different items, and you compare them. The main question a bar graph answers is: "What is the measurement for each item?"

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