- 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 of Human Geography
- Fields and Sub-fields of Human Geography
- Overview of Human Geography - Nature and Scope
Unit I
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
Population Distribution, Density, Growth and Composition
Human Settlements
The World Population Density, Distribution and Growth
- Population Distribution in the World
- Density of Population
- Factors Influencing the Distribution of the Population
- Population Growth and Growth Measures
- Components of Population Change
- Demographic Transition
- Population Control Measures
Unit II
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
Human Development
- Growth and Development
- Concept of Human Development
- Approaches of Human Development
- Measuring Human Development
- International Comparisons of Human Development
Unit III
Land Resources and Agriculture
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
Water Resources
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
Primary Activities
- Hunting and Gathering
- Pastoralism
- Agricultural Systems
- Mining
Map Work (Based on identification of features on World Political Map)
Unit I
Mineral and Energy Resources
Secondary Activities
Tertiary and Quaternary Activities
Unit II
Planning and Sustainable Development in Indian Context
Transport, Communication and Trade
Unit III
Transport and Communication
International Trade
International Trade
Unit IV
Unit V
Geographical Perspective on Selected Issues and Problems
Map Work (Based on locating and labelling on a political map of India)
Geography Practical II
Practical Record Book and Viva Voce
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.
