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.
Contact Us