Descriptive Statistics in Quantitative Reasoning: Central Tendency

Central Tendency (Mean, Median, and Mode) and Outliers in Descriptive Statistics 

Central tendency in Descriptive Statistics refers to a single value that represents the center or typical performance of a dataset. In education, it helps teachers quickly understand how a class is performing overall.

The three main measures are:

• Mean (Average)

• Median (Middle Value)

• Mode (Most Frequent Value)

📊 1. Mean (Average)

Definition: The mean is calculated by adding all scores and dividing by the total number of students.

Formula:

$$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$$

Example:

Scores: 60, 70, 75, 80, 90

Mean = (60 + 70 + 75 + 80 + 90) ÷ 5 = 75

✅ Use in B.Ed:

• Helps teachers judge the overall academic level of the class.

• Useful for comparing performance across different sections.

⚠️ Limitation:

The mean is affected by extremely high or low scores (outliers).

📊 2. Median (Middle Score)

Definition: The median is the middle value when scores are arranged in ascending or descending order.

Steps:

1. Arrange scores from lowest to highest.

2. Find the middle number.

Example:

Scores: 50, 65, 70, 85, 95

Median = 70

If there are two middle values, average them.

✅ Use in B.Ed:

• Best indicator of “typical” performance when scores vary widely.

• Not affected much by extreme scores.

📊 3. Mode (Most Frequent Score)

Definition: The score that appears most often.

Example:

Scores: 55, 65, 65, 70, 80

Mode = 65

✅ Use in B.Ed:

• Shows the score most students achieved.

• Helps identify common learning levels.

⚠️ A dataset may have:

• One mode (unimodal)

• Two modes (bimodal)

• No mode

🚨 Identifying Outliers

Outliers are scores that are significantly higher or lower than the rest.

Example:

Scores: 65, 68, 70, 72, 20

👉 The score 20 is an outlier.

Why Outliers Matter:

• They can distort the mean.

• May indicate:

• Learning difficulties

• Test anxiety

• Absenteeism

• Assessment errors

🎓 B.Ed Classroom Application

When analysing end-of-unit test scores:

• Mean → Overall class performance

• Median → Typical student achievement

• Mode → Most common learning level

• Outliers → Students needing attention or enrichment

👉 Using all three gives a more accurate picture than relying on just one measure.

📊 Differences Table (Mean vs Median vs Mode)

Feature	Mean	Median	Mode
Definition	Average of all scores	Middle value	Most frequent score
Affected by Outliers?	✅ Yes (strongly)	❌ No	❌ No
Best Used When	Scores are evenly distributed	Scores are skewed	Identifying common performance
Shows	Overall class level	Typical student	Most common achievement
Easy to Calculate?	Moderate	Easy	Very Easy
Limitation	Can be misleading with extreme scores	Does not use all data	May not exist

✍️ By: Raja Bahar Khan Soomro 

Further Suggested Readings 

INTRODUCTION TO CURRICULUM & ITS MAIN TYPES

FOUNDATIONS OF CURRICULUM DEVELOPMENT

Major Curriculum Development Ideologies and the National Curriculum of Pakistan

Comparative Analysis of Linear Curriculum Models: Tyler vs. Taba in the Context of Sindh

Data Production and Visualisation in Quantitative Reasoning Course