What is a box and whisker plot?

• A box and whisker plot is a visual representation of how data is spread out and how much variation there is. It doesn’t show all the data values, but instead focuses on the median, extremes, and quartiles.

MedianThe median is the middle value of an ordered set of numbers. (If the numbers are not in order from least to greatest, do this first!)

Example: 2 3 7 11 14In this case, the median is 7.

*Note: If there are 2 middle numbers, add and divide by 2

Example: 2 3 7 11 14 19The median is 9.

Extremes

The extremes are the highest and lowest values of the data set.

Example: 2 3 7 11 14

In this case, the lower extreme is 2 and the upper extreme is 14.

Quartiles

The quartiles are the median of the higher half of the data set and the median of the lower half of the data set.

Example: 2 3 7 11 14In this case, the lower quartile is

2.5 (2 + 3 = 5…5/2 = 2.5).

Theupper quartile is 12.5 (11 + 14 = 25…25/2 = 12.5).

Let’s Do an Example Together…

We’ll use the data we used when making a stem and leaf plot earlier: the temperature every day for the month of August.

Step 1• There are 31 days in August, and here are the temperatures for that

month:

August 76 82 83 90 93 85 78 75 71 71 72 69 70 75 77 83 85 82 80 81 77 76 78 74 72 73 77 77 76 77 72

• The first step is to take these data values and put them in order from least to greatest.

- Example:69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77 77 77 77 78 78 80 81 82 82 83 83 85 85 90 93

Step 2

• The second step is to find the extremes. Remember, the lower extreme is the lowest value and the upper extreme is the highest value.

-Example:69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77 77 77 77 78 78 80 81 82 82 83 83 85 85 90 93

Lower Extreme: 69Upper Extreme: 93

Step 3

• The third step is to find the median. Remember, the median is the middle value.

-Example:69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77 77 77 77 78 78 80 81 82 82 83 83 85 85 90 93

There are 31 values, therefore the median is the 16th value: 77. (There are 15 values

below it, and 15 values above it.)

Step 4

• The fourth step is to find the lower quartile. Remember, this is the median of the lower half of the data.

-Example:

69 70 71 71 72 72 72 73 74 75 75 76 76 76 77

There are 15 values; therefore the median is the 8th value: 73. (There are 7 values below it, and 7 values above it.)

Step 5

• The fifth step is to find the upper quartile. Remember, this is the median of the upper half of the data.

-Example:

77 77 77 78 78 80 81 82 82 83 83 85 85 90 93

There are 15 values; therefore the median is the 8th value: 82. (There are 7 values below it, and 7 values above it.)

Step 6

• The sixth step is to plot the extremes (lower extreme 69, upper extreme 93),

• the quartiles (lower quartile 73 and upper quartile 82),

• and the median (77) on a number line.

-Example:

Step 7

• The seventh step is to draw a rectangular box extending from the lower quartile to the upper quartile.

• Indicate the median with a vertical line extending through the box.

-Example:

Step 8

• The eighth step is to connect the lower extreme to the lower quartile with a line (one "whisker") and the upper quartile to the upper extreme with another line (the other "whisker”).

-Example:

Completion!!!

• You have just finished your very own box and whisker plot! Congratulations! Remember to add a title and a key. Here is what your final product should look like:

Temperatures for August

Key:75 = 75 degrees Fahrenheit

What does the graph tell you?

• Well, you can see that the lowest temperature in August was 69 degrees Fahrenheit and the highest temperature was 93 degrees Fahrenheit.

• This gives you the range of the data: 24. (93-69 = 24)

• You also know that the median or middle value is 77 degrees Fahrenheit.

• Since the medians (3 of them) represent the middle points, they split the data into 4 equal parts.– One quarter of the data numbers are less than 73 – One quarter of the data numbers are between 73 and 77– One quarter of the data numbers are between 77 and 82 – One quarter of the data numbers are greater than 82

A Special Case

• At some point you might see a box and whisker plot that has an asterisk like the example below. Sometimes there is one piece of data that falls way outside the range of the other values.

• This piece of data is called an outlier, and it’s shown by an asterisk in a box and whisker plot.