Example of Box and Whisker Plot

Example:

Suppose we have a dataset representing the test scores of a group of students: Data (test scores): 78, 85, 90, 92, 95, 96, 97, 98, 99, 100, 105, 110, 120.

Solution:

Step 1: Collect Data

Dataset: 78, 85, 90, 92, 95, 96, 97, 98, 99, 100, 105, 110, 120

Step 2: Calculate Quartiles

To create a Box and Whisker Plot, we need to calculate the quartiles (Q₁ and Q₃) and the median (Q₂).

-Q1 (the first quartile) is the median of the lower half of the data (78, 85, 90, 92, 95, 96) = 91

-Q2 (the median) is the median of the entire dataset = 97

-Q3 (the third quartile) is the median of the upper half of the data: (98, 99, 100, 105, 110, 120) = 102.5

Step 3: Determine Whiskers

To find the whiskers, calculate the minimum and maximum values within the dataset, excluding potential outliers.

Minimum = 78, Maximum = 120

The required five-number summary is 78, 91, 97, 102.5, 120.

Step 4: Plot the Box and Whiskers

Now, we can create the Box and Whisker Plot:

-Draw a box from Q₁ (91) to Q₃ (102.5).

-Draw a line inside the box at Q₂ (97).

-Extend the left whisker from the minimum (78) to Q₁ (91).

-Extend the right whisker from Q₃ (102.5) to the maximum (120).

Step 5: Identify Outliers

Any data points that fall outside the whiskers are considered outliers. In this case, we do not have any outliers. This Box and Whisker Plot gives a visual rundown of the grades, showing the middle (Q₂) at 97, the interquartile range (IQR) from Q₁ to Q₃ (91 to 102.5), and the shortfall of exceptions. It successfully outlines the focal propensity, spread, and dissemination of the dataset.