Understanding Mean, Median, and Mode

Descriptive statistics are essential for summarizing and interpreting data. When dealing with a dataset, three key measures of central tendency often come into play: mean, median, and mode. Each of these measures provides unique insights into the characteristics of a dataset. Below are three practical examples showcasing how to calculate each of these statistics in different contexts.

Example 1: Calculating the Mean in a Classroom

In a classroom setting, a teacher wants to assess the average score of her students on a recent math test. The scores of the students are as follows: 78, 85, 92, 88, 76.

To calculate the mean:

1. Add all the scores together: 78 + 85 + 92 + 88 + 76 = 419.
2. Divide the total by the number of students: 419 / 5 = 83.8.

The mean score of the class is 83.8. This average helps the teacher gauge overall performance and identify areas for improvement.

Notes:

• The mean is sensitive to extreme values (outliers). If one student scored 50, the mean would decrease significantly.

Example 2: Finding the Median in a Real Estate Market

A real estate agent is analyzing the sale prices of houses in a neighborhood to determine the median price. The sale prices (in thousands) are: 150, 200, 250, 300, 400.

To find the median:

1. Arrange the values in order (which they already are): 150, 200, 250, 300, 400.
2. Since there is an odd number of observations (5), the median is the middle number: 250.

The median sale price is 250, which gives a better indication of a typical sale price than the mean, especially if there are extreme values.

Notes:

• If the dataset had an even number of values, you would average the two middle numbers to find the median.

Example 3: Identifying the Mode in a Survey

A company conducts a survey to find out the preferred mode of transportation among its employees. The responses are as follows: Car, Bus, Car, Train, Car, Bus.

To find the mode:

1. Count the frequency of each response:

• Car: 3
• Bus: 2
• Train: 1
  
  2. The response with the highest frequency is the mode.

The mode of transportation among employees is Car, indicating that most employees prefer to drive to work.

Notes:

• A dataset can have more than one mode (bimodal or multimodal) if multiple values occur with the same highest frequency. If all values occur with the same frequency, the dataset is considered to have no mode.