A bar graph tells you how many objects in a given category you have. For example, in the following bar graph:

Each bar tells you how many children fall into that height range. So, for example, there are 2 children between 0 and 4 feet; there are 7 between 4 feet 1 inch and 4 feet 6 inches, and so on.

__Example 1__

How many children are between 4 feet 7 inches and 6 feet? How many children are taller than 6 feet?

Answer
To find how many children are between 4'7 and 6', we just need to add up the children whose heights are between 4'7 - 5', 5'1 - 5'6, and 5'7 - 6'. Thus, we get children.

Looking at the bar graph, we see that there are no children taller than 6 feet. So the answer is 0.

We can also have segmented bar graphs like the following:

These bar graphs allow us to compare different groups, in this case the group of 1 year olds against the group of 2 year olds, 3 year olds, and so on. We can thus see how their preferences shift over time.

To read the graph, the horizontal signs tell us which categories we have (here, the different ages 1 to 5) and then the vertical component tell us how many members of that category (e.g. how many one year-olds) in accordance with the key to the right. Thus, the left-most blue bar tells us how many 1 year-olds have "Mighty Man" as their favorite superhero. The right-most yellow bar tells us how many 5 year-olds have "Valiant Vanessa" as their favorite hero and so on.

__Example 2__

Which superhero gains the most fans as the children mature from being 1 years-old to 5 years-old?

Answer
We look at how many fans each has among the 1 years-old and among the 5 years-old:

One-Years Old

Mighty Man: 9

Speedy Sally: 10

Tornado Terry: 3

Valiant Vanessa: 8

Five-Years Old

Mighty Man: 5

Speedy Sally: 8

Tornado Terry: 9

Valiant Vanessa: 8

Thus, the changes in popularity are as follows:

Mighty Man: -4

Speedy Sally: +2

Tornado Terry: 6

Valiant Vanessa: 0

So Tornado Terry gains the most fans.

**Example 3**

Which superhero has the most supporters overall (i.e. across all the age groups)?

Answer
We can just add up the supporters for each superhero across the different age groups. Doing so, we get:

Mighty Man:

Speedy Sally:

Tornado Terry:

Valiant Vanessa:

Thus, Mighty Man has the most supporters overall.

**Example 4**

Which of the following tables goes with the given bar graph:

A.

B.

C.

D.

Answer
To answer this question, we just need to understand how to read a bar graph. The left-hand column in each table corresponds to the different categories, while the right-hand column gives the number of people that fit in that category. Thus the left-hand side corresponds to the label below each bar on the bar graph and the right-hand side corresponds to the height of the bar.

Going through each row of the the tables, we find that only C matches the bar graph above.

**Practice Problems**

- Which of the following tables is compatible with the given graph?

A.

B.

C.

D.

Answer

We just need to check, for each range, how many people in the bar graph fit into the specified range. Thus, for example, between 5'1 and 6', we have 8 students. Going through the different tables, we conclude that only B matches the data.

- A new kid, Richard, joins the class. Richard is 4'8. Given that the graph below accurately depicts the heights of Richard's classmates, what is the maximum possible number of classmates that are taller than Richard? What is the minimum possible number?
Answer

We know that every kid that is 5'1 or taller will be taller than Richard. Thus, at a minimum, 8 people have to be taller than Richard. But it is not clear how many of the children between 4'7 and 5' are taller than Richard. If none of them are, then 8 people will be taller than Richard. If all of them are, then 17 people will be taller than Richard. Thus, the maximum possible number is 17 and the minimum possible number is 8.

- In the below chart, what percentage of three-year olds take Tornado Terry to be their favorite hero?

Answer

There were 30 three-year olds surveyed and 10 of them reported Tornado Terry was their favorite. Thus, the percentage is 33%.

- In the below chart, which superhero loses the most fans as children age from 1 to 5?

Answer

We just need to go through each of the heroes to find which loses the most fans. Mighty Man loses 4 fans; Speedy Sally loses 2 fans; and Tornado Terry/Valiant Vanessa both lose no fans. Thus, Mighty Man loses the most fans.

- In the below chart, what if anything can you conclude about the median height of the class?

Answer

While you cannot conclude the exact value of the median, you know that it must occur somewhere in the range of 4'7 to 5'. That is because you know that there are 9 students shorter than 4'7 and removed students at either extreme, you would have to end up with someone in the 4'7 to 5' range.

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