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- minimum value
- maximum value
- median
- first quartile
- third quartile

Box plots are visual illustrations of this information.

A box plot provides a visual approximation of the distribution of a data set since each segment of the chart contains one quarter, or $25%$ of the data. Note that the center $50%$ of the data lies inside the box. The further apart the segments are, the greater the spread is for that quarter of the data.

Thanks a Latte Café measured the temperature of 800 cappuccinos. The box plot below shows the results in $_{∘}$F.

A good cappuccino, according to the experts, has a temperature between $131_{∘}$F and $140_{∘}$F. Approximately how many of the cappuccinos could be considered "good"?

Show Solution

Each part of a box plot contains $25%$ of the data. This means the box contains $50%$ of the data.

The first quartile is located at 129 degrees and the third is at 140 degrees. This means that

0.50⋅800=400.

Approximately 400 cappuccinos can be considered "good".
Because a box plot shows the minimum, maximum, median, and first and third quartiles these need to be identified from the data set. The following data set gives the test scores for a grade.
### 1

Sometimes, the data will be given in ascending order. When it is not, it's necessary to order the data so the quartiles can be found.
With an ordered data set, the minimum and maximum are easily identifiable. Here, the minimum is 5 and the maximum is 16. These are marked above a number line with a line segment, indicating the range.
### 2

Since there are 26 values, the median is the mean of the numbers at the 13th and 14th position.
Now, the median can be determined by calculating the mean of 11 and 11.5.
The median is 11.25. This is marked as a vertical line segment in the range. Remember that the line for the median falls inside the box.
### 3

Lastly, find the first and third quartiles. The median divides the set into two smaller sets each with 13 values. The first quartile is the middle value in the lower set: 8.5.
The third quartile is the median of the upper set: 13.5.

Order the data set, then find the minimum and maximum

Determine the median

Determine the quartiles

The quartiles are marked as the sides of the box plot. Now the box plot is complete.

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