qoount

 

1. Mean, Median and Mode (with Standard Deviation)

Mean:
Mean is the arithmetic average of a set of observations.

xˉ=∑xn\bar{x}=\frac{\sum x}{n}

It is rigidly defined and based on all observations.

Median:
Median is the middle value when data are arranged in ascending or descending order.
It divides the data into two equal parts.

Mode:
Mode is the value which occurs most frequently in the data.
It is useful in finding the most common item.

Standard Deviation:
Standard deviation measures the dispersion of data from the mean.

σ=∑(x−xˉ)2n\sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n}}

It shows the consistency and variability of data.

2. Karl Pearson’s Coefficient of Correlation

Karl Pearson’s coefficient measures the degree and direction of linear relationship between two variables.

r=∑xy∑x2∑y2r=\frac{\sum xy}{\sqrt{\sum x^2 \sum y^2}}

Properties:

  • −1≤r≤+1-1 \le r \le +1

  • r=+1r=+1: perfect positive correlation

  • r=−1r=-1: perfect negative correlation

  • r=0r=0: no correlation

It is widely used in statistics and economics.

3. Matrices and Solution of Equations

A matrix is a rectangular array of numbers arranged in rows and columns.

Solution of simultaneous equations using matrices:
Given

AX=BAX=B

Then

X=A−1B(if ∣A∣≠0)X=A^{-1}B \quad (\text{if } |A|\neq0)

Matrices make solving linear equations easy and systematic.

4. Scope, Nature and Importance of Statistics

Scope of Statistics:

  • Economics

  • Business and Commerce

  • Government planning

  • Social sciences

Nature of Statistics:

  • Deals with aggregates of facts

  • Expressed numerically

  • Affected by multiple causes

Importance of Statistics:

  • Helps in decision making

  • Simplifies complex data

  • Useful in forecasting and planning

5. Matrices: Types, Scope, Nature and Importance

Types of Matrices:

  • Row matrix

  • Column matrix

  • Square matrix

  • Zero matrix

  • Identity matrix

Scope:

  • Economics

  • Engineering

  • Computer science

Nature:

  • Mathematical representation of data

  • Operates under fixed rules

Importance:

  • Solves linear equations

  • Used in business analysis

  • Helpful in scientific calculations

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