A histogram looks a lot like a bar graph and, indeed, you can think of it as a special kind of bar graph. But instead of having just any kind of category (as a bar graph does), histograms have, as their categories, certain ranges of values. So, for example, suppose the students in your class score the following scores on their test:
Now, those numbers are kind of unwieldy. So to get a sense of how many students are acing your class (getting an A) or failing your class (getting an F), you might categorize their test scores according to certain ranges. So put all the 90100 scores together in one category, all the 80  89 scores in the same category, and so on. Graphing this, we would get the following:
This graph tells us that 4 students scored between 90 and 100; 3 students between 80 and 89; and so on.
Example 1
In the following histogram, approximately how many students scored a 170 or higher?
Answer
We simply add up the number that fall in ranges of 170  172.9, 172.9  175.8, and so on. Doing so, we get: . It's a little hard to see what the exact value are just based on the graph, so anything from 126 and 136 would be reasonable.
Example 2
In the below histogram, what if anything can we conclude about the median of the data?
Answer
We cannot conclude the exact median, but we know that it will be between 80 and 89. This is because there are four students above that range and there are two students below that range. So the median must be the average of two values between 80 and 89.
Example 3
In the following chart, what can we conclude about the range of the data?
Answer
We don't know the exact range but we can give some values that the range must lie in between. We know that the minimum value is somewhere between 141 and 143.9. We know that the maximum value is somewhere between 178.7 and 181.6. Subtracting the smallest possible minimum value from the largest possible maximum, we get . Subtracting the largest possible minimum from the smallest possible maximum, we get Those are our maximum and minimum possible ranges, respectively. The true range must lie between them.
Practice Problems
 In the following histogram, approximately how many students scored a 170 or lower?
Answer
We simply sum up over the various ranges that are smaller than 170. Thus, we get: 1 + 2 + 1 + 2 + 12 + 21 + 42 = 81 as an approximation of the number of students that scored a 170 or lower.

In the below histogram, what if anything can we conclude about the range of the data?
Answer
Because the fourth column is simply labeled <70, we can only conclude that the range is at least 21 (since it is possible to have students get no higher than 90 and no lower than 69).
 In the below histogram, what is the minimum possible number of students who scored higher than 75? What about the maximum?
Answer
To get the minimum possible number of students who scored higher than 75, we suppose that everyone who scored in the 70 to 79 range got below a 75. Then, we get that 7 students scored higher than a 75. To get the maximum possible number, we suppose that those students all scored higher than 75. Then, we get that 8 students scored higher than a 75.
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