**What is Central Tendency?**

Central Tendency refers to the measure that identifies the center or the** “middle”** of a dataset.

It gives us a single value that represents the entire set of data.

**Example**

In this case, the “middle” can be represented in three ways: **Mean,** **Median**, and **Mode**.

Imagine you have the test scores of a class: 85, 90, 88, 78, 92.

The Mean (commonly known as Average) for these test scores is 86.6, the Median is 88, and the Mode is (as calculated by Chat GPT).

**3 Types of Central Tendency**

- Mean(Average)
- Median
- Mode

There are 3 types of central tendency. Let me explain about their overalls and how to calculate them.

**1. Mean**

It’s the average. **You sum up all the numbers and then divide by the total count.**

*Formula*:

Attention: This formula looks too complex, but remember, **all you need to do** is to sum up all the numbers, then divide by the total count.

For scores 85, 90, 88, 78, 92, the mean is:

**2. Median**

The number right in the middle when data is arranged in order. If the dataset has an odd number of observations,** the median is the middle number. **

**If it has an even number of observations, the median is the average of the two middle numbers.**

For scores 78, 85, 88, 90, 92, the median is 88.

**3. Mode**

The number that appears most often. There isn’t a mathematical formula for the mode. It’s determined by **frequency**.

In the scores 85, 85, 88, 90, 92, the mode is 85 as it appears twice.

**Mean vs Median**

Beginners often mistakenly believe that the Mean (or average) accurately represents the center of any statistical data.

**However, the Mean isn’t universally applicable.** In some cases, using the Median as a central measure might be more appropriate.

**Mean: When to Apply?**

Mean is good to apply **when data is symmetrically distributed without outliers.**

**Inappropriate Scenario 1**

In the presence of extreme outliers.

For instance, when determining the **average income** in a neighborhood,** if a billionaire lives there**, the mean might be skewed and not represent the typical resident’s income.

Outliers can heavily skew the mean, making it less representative of the majority of data points.

**Inappropriate Scenario 2**

When data is bimodal or has multiple peaks.

For example, if a class has **two distinct groups of high and low scorers**, the mean might not accurately represent either group.

The mean can be influenced by the distribution of data and might not capture the essence of bimodal distributions.

**Median: When to Apply?**

Median is good to appply **when data has outliers or is skewed**.

**Inappropriate Scenario 1**

When data has gaps or is open-ended. **For instance, age categories like “60 and above” can make it challenging to determine a precise median.**

Without specific data points, finding an exact middle value becomes difficult.

**Inappropriate Scenario 2**

When data is ordinal **but** **the intervals between categories aren’t consistent**.

For example, a survey with responses like “not at all”, “somewhat”, “very much” might not have equidistant intervals.

**Exercises: Which to Apply, Mean or Median?**

To help you grasp these concepts, here are three statistical cases. Decide whether the Mean or Median would be more appropriate:

**Case 1**

**A shoe company wants to determine the average shoe size of its customers.**

The sizes range from 5 to 12, but there’s a promotional event where customers with size 11 shoes get a significant discount.

**Case 2**

A city wants to determine the central age of its residents.

**However,** there’s a renowned university in the city, leading to a higher population of people aged 18-22.

**Case 3**

A survey asks people how many times they eat out in a week.

Most responses are between 1-3 times, but **a few respondents claim they eat out every meal, totaling 21 times a week**.

**Answers**

**Median**: Due to the promotional event, there might be a disproportionate number of size 11 shoe sales, which could skew the mean.**Median**: The influx of university students can create a peak in the data, making the median a better representative of the central age.**Mean**: Despite some high numbers, this data is likely to be symmetrically distributed, making the mean a suitable measure.