Statistics Class Notes (Mean, Median, Mode)
Topic: **Measures of Central Tendency (Mean, Median, Mode)**
Introduction
Statistics is the science of **collecting, analyzing, interpreting, and presenting data**. One of the
most important aspects of statistics is **data summarization**. Since large sets of data can be
complex, we need tools that allow us to represent data in a simpler form without losing essential
information.
**Measures of Central Tendency** are statistical tools that represent the **center** or **typical
value** of a dataset. These measures help us understand where most of the data points tend to
cluster.
The three most commonly used measures are:
1. **Mean** (Arithmetic Average)
2. **Median** (Middle Value)
3. **Mode** (Most Frequent Value)
Importance of Measures of Central Tendency
* Provide a single representative value for the dataset.
* Make data comparison easier.
* Help in decision-making (business, economics, research, etc.).
* Useful in analyzing survey results, exam scores, economic data, and scientific experiments.
1. Arithmetic Mean
Definition
The arithmetic mean is the **sum of all values divided by the number of values**.
**Formula:**
, Mean {X} ={Sum of all values}} / {{Number of values}}
Example (Ungrouped Data):
Marks of 5 students = 10, 20, 30, 40, 50
{X} ={10+20+30+40+50}{5} ={150} / {5} = 30
So, the mean = 30.
Mean for Grouped Data
**Formula (Discrete frequency distribution):**
{X} = { fixi} / { fi }
Where:
* xi = data values
* fi = frequencies
**Example:**
Class intervals and frequencies:
| Class | Frequency (f) | Midpoint (x) | f × x |
| ----- | ------------- | ------------ | ----- |
| 0–10 | 3 |5 | 15 |
| 10–20 | 5 | 15 | 75 |
| 20–30 | 7 | 25 | 175 |
| 30–40 | 5 | 35 | 175 |
| 40–50 | 4 | 45 | 180 |
{X} = { (fx) /f }
Topic: **Measures of Central Tendency (Mean, Median, Mode)**
Introduction
Statistics is the science of **collecting, analyzing, interpreting, and presenting data**. One of the
most important aspects of statistics is **data summarization**. Since large sets of data can be
complex, we need tools that allow us to represent data in a simpler form without losing essential
information.
**Measures of Central Tendency** are statistical tools that represent the **center** or **typical
value** of a dataset. These measures help us understand where most of the data points tend to
cluster.
The three most commonly used measures are:
1. **Mean** (Arithmetic Average)
2. **Median** (Middle Value)
3. **Mode** (Most Frequent Value)
Importance of Measures of Central Tendency
* Provide a single representative value for the dataset.
* Make data comparison easier.
* Help in decision-making (business, economics, research, etc.).
* Useful in analyzing survey results, exam scores, economic data, and scientific experiments.
1. Arithmetic Mean
Definition
The arithmetic mean is the **sum of all values divided by the number of values**.
**Formula:**
, Mean {X} ={Sum of all values}} / {{Number of values}}
Example (Ungrouped Data):
Marks of 5 students = 10, 20, 30, 40, 50
{X} ={10+20+30+40+50}{5} ={150} / {5} = 30
So, the mean = 30.
Mean for Grouped Data
**Formula (Discrete frequency distribution):**
{X} = { fixi} / { fi }
Where:
* xi = data values
* fi = frequencies
**Example:**
Class intervals and frequencies:
| Class | Frequency (f) | Midpoint (x) | f × x |
| ----- | ------------- | ------------ | ----- |
| 0–10 | 3 |5 | 15 |
| 10–20 | 5 | 15 | 75 |
| 20–30 | 7 | 25 | 175 |
| 30–40 | 5 | 35 | 175 |
| 40–50 | 4 | 45 | 180 |
{X} = { (fx) /f }
