- Measures of Central Tendency are statistical methods used to find a single value that represents the entire data set. They are also called averages.
- The main measures are Mean, Median and Mode.
- Mean (Arithmetic Average) = Sum of all values ÷ Number of observations.
It represents the overall average of the data. - Median = The middle value when data is arranged in ascending or descending order.
If the number of observations is even, median is the average of the two middle values. - Mode = The value that occurs most frequently in the data set.
It shows the most common value in the distribution.
Topics
Human Geography - Nature and Scope
- Introduction to Human Geography Nature and Scopes
- Nature of Human Geography
- Scopes of Human Geography
- Overview of Human Geography - Nature and Scope
Population : Distribution, Density, Growth and Composition
- Distribution of Population in India
- Density of Population
- Regional Variation in Population Growth
- Population Composition
- Promoting Gender Sensitivity
- Overview of Population : Distribution, Density, Growth and Composition
Fundamentals of Human Geography
Data – Its Source and Compilation
- What is Data?
- Need of Data
- Presentation of Data
- Sources of Data
- Sources of Data - Primary
- Sources of Data - Secondary
- Tabulation and Classification of Data
- Data Compilation and Presentation
- Processing of Data
- Grouping of Data
- Process of Classification
- Overview of Data – Its Source and Compilation
Human Settlements
- Human Settlements
- Concept of Rural Settlements
- Types of Rural Settlements
- Concept of Urban Settlements
- Urbanisation in India
- Overview of Human Settlements
India - People and Economy
The World Population - Distribution, Density and Growth
- The World Population - Distribution, Density and Growth
- Patterns of Population Distribution in the World
- Density of Population
- Factors Influencing the Distribution of the Population
- Doubling Time of World Population
- Spatial Pattern of Population Change
- Impact of Population Change
- Theories of Population Growth
- Population Control Measures
- Overview of The World Population - Distribution, Density and Growth
Data Processing
- Mode
- Comparison of Mean, Median and Mode
- Methods of Measuring Dispersion
- Rank Correlation
- Direction of Correlation
- Method of Calculating Correlation
- Degree of Correlation
- Overview of Data Processing
Graphical Representation of Data
- General Rules for Drawing Graphs, Diagram and Maps
- Construction of Diagrams
- Classification of Thematic Maps Based on Method of Construction
- Overview of Graphical Representation of Data
Human Development
- Concept of Human Development
- Growth and Development
- Four Pillars of Human Development
- Approaches of Human Development
- Measuring Human Development
- International Comparisons
- Overview of Human Development
Geography Practical II
Land Resources and Agriculture
- Land Resources and Agriculture
- Land Uses Categories
- Land Use Changes in India
- Common Property Resources
- Agriculture Land Use in India
- Agricultural Development in India
- Problems of Indian Agriculture
- Overview of Land Resources and Agriculture
Spatial Information Technology
- Spatial Information Technology
- Geographical Information System (GIS)
- Advantage of GIS Over Manual Methods
- Components of GIS
- Spatial Data Formats
- Sequences of GIS Activities
- Overview of Spatial Information Technology
Water Resources
- Concept of Water Resources
- Water Resources of India
- Deterioration of Water Quality
- Water Conservation Practices > Watershed Management
- Overview of Water Resources
Primary Activities
- Introduction to Primary Activities
- Hunting and Gathering
- Pastoralism
- Agriculture
- Mining
- Overview of Primary Activities
Mineral and Energy Resources
- Mineral and Energy Resources
- Types of Minerals in India
- Distribution of Minerals in India
- Conservation of Minerals
- Overview of Mineral and Energy Resources
Secondary Activities
- Introduction to Secondary Activities
- Manufacturing
- Household Industries Or Cottage Manufacturing
- Industries Based on Ownership
- Overview of Secondary Activities
Planning and Sustainable Development in Indian Context
Tertiary and Quaternary Activities
- Tertiary and Quaternary Activities
- Types of Tertiary Activities
- People Engaged in Tertiary Activities
- Some Selected Examples
- Quaternary Activities
- Quinary Activities
- The Digital Divide
- Overview of Tertiary and Quaternary Activities
Transport and Communication
- Communication
- Land Transport
- Oil and Gases Pipelines
- Communication Networks
- Overview of Transport and Communication
Transport and Communication
- Communication
- Transport
- Mode of Transport
- Water Transport
- Air Transport
- Pipelines
- Overview of Transport and Communication
International Trade
- Concept of Trade
- Changing Pattern of the Composition of India's Exports
- Changing Patterns of the Composition of India's Import
- Sea Ports as Gateways of International Trade
- Air Routes of International Trade
- Overview of International Trade
International Trade
- Concept of Trade
- History of International Trade
- Gateway of International Trade
- Overview of International Trade
Geographical Perspective on Selected Issues and Problems
- Urban Waste Disposal
- Rural-urban Migration
- Problems of Slums
- Land Degradation
- Overview of Geographical Perspective on Selected Issues and Problems
Estimated time: 24 minutes
CBSE: Class 12
Key Points: Measures of Central Tendency
CBSE: Class 12
Key Points: Computing Mean from Ungrouped Data
- Direct Method: Mean is calculated by adding all the values and dividing by the total number of observations.
- In the direct method, raw data is used directly without any changes.
- Indirect Method is used when there are large numbers or big values, to make calculation easier.
- In the indirect method, an assumed mean is selected and each value is reduced by subtracting this constant (coding method).
- The final mean calculated by both direct and indirect methods is the same, only the calculation process is different.
CBSE: Class 12
Formula: Mean Under Ungrouped Data(Direct Method)
\[\overline{\mathrm{X}}=\frac{\sum x}{\mathrm{N}}\]
CBSE: Class 12
Formula: Mean (Indirect Method) Under Ungrouped Data
\[\overline{\mathrm{X}}=A+\frac{\sum d}{N}\]
CBSE: Class 12
Key Points: Computing Mean from Grouped Data
- In grouped data, individual values are not shown separately. Therefore, the midpoint (class mark) of each class interval is used to calculate the mean.
- Direct Method: Multiply each class midpoint (x) with its frequency (f), find ∑fx, and divide by total frequency (N).
- Indirect Method: An assumed mean (A) is taken from a middle class to simplify calculation. Deviations (d) are calculated from A and multiplied by frequency (f).
- If class intervals are equal, shortcut method using interval width can also be applied.
- Both direct and indirect methods give the same mean, but the indirect method is easier when data values are large or calculations are lengthy.
CBSE: Class 12
Formula: Mean (Direct Method) Under Grouped Method
\[\begin{array}
{rcl}{\overline{\mathbf{X}}} & {=} & {\sum fx}
\end{array}\]
CBSE: Class 12
Formula: Mean (Indirect Method) Under Grouped Method
\[\bar{x}=A\pm\frac{\sum fd}{N}\]
CBSE: Class 12
Key Points: Median
- Median is a positional average, meaning it depends on the position of values in a data set.
- It is the middle value that divides the data into two equal parts.
- Median is represented by the symbol M.
- For ungrouped data, the values must first be arranged in ascending or descending order.
- If the number of observations is odd, the median is the exact middle value.
- If the number of observations is even, the median is found by taking the average of the two middle values.
- For grouped data, median is found by using the cumulative frequency table, and the class where the middle observation lies is called the median class.
CBSE: Class 12
Formula: Median Under Ungrouped Data
\[\mathrm{Value~of}\left(\frac{\mathbf{N}+1}{2}\right)\mathrm{th~item}\]
CBSE: Class 12
Formula: Median Under Grouped Data
\[M=\quad l+\frac{i}{f}\left(\frac{N}{2}-c\right)\]
CBSE: Class 12
Key Points: Mode
- Mode is the value that occurs most frequently in a data set.
- It is represented by Z or M₀.
- Mode is less commonly used compared to mean and median.
- To find mode in ungrouped data, values are first arranged in ascending or descending order to easily spot repeated values.
- A data set can be unimodal (one mode), bimodal (two modes), trimodal (three modes), multimodal (many modes), or have no mode if no value repeats.
CBSE: Class 12
Key Points: Comparison of Mean, Median and Mode
- The comparison of mean, median and mode can be understood using a normal distribution curve, which is bell-shaped and symmetrical.
- In a normal distribution, the mean, median and mode are equal and lie at the centre of the distribution.
- Most of the observations are concentrated around the middle value, while very high and very low values are rare.
- The normal curve is symmetrical, meaning half of the values lie above the centre and half lie below it.
- When data is skewed (not symmetrical), the mean, median and mode do not coincide and their values differ.
