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Classic

Statistics

Introduction

What is statistics ?

Set of scientific methods aimed at collecting, organizing, presenting, modelling data and constructing numerical summaries.

Statistics:
   - Numerical data (e.g. consumption of French households)
   - Non-numerical data (e.g. marital situation)

Measures of central tendency

Central tendency describes the tendency of the observations to bunch around a particular value or category

Three ways:
   - Mean (average)
   - Median (middle value)
   - Mode (most frequent value)

Mean

MEAN = AVERAGE

Add up all the numbers and divide by how many numbers there are


Formula: xˉ=∑i=1nxin\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}

Median

MEDIAN = MIDDLE VALUE

Put the numbers in ascending order and find the middle value. If there are two middle values, take the average of the two.

Formula:

Median={xn+12if n is oddxn2+xn2+12if n is evenMedian = \begin{cases}x_{\frac{n+1}{2}} & \text{if n is odd} \\\\\\\\ \frac{x_{\frac{n}{2}} + x_{\frac{n}{2} + 1}}{2} & \text{if n is even}\end{cases}

Mode

MODE = MOST FREQUENT VALUE

Most commonly occuring number.

Measures of dispersion

Dispersion describes the spread of the observations around the central tendency

Three ways:
   - Range (difference between the largest and smallest values)
   - Variance (average of the squared deviations from the mean)
   - Standard deviation (square root of the variance)

Range

RANGE = DIFFERENCE BETWEEN THE LARGEST AND SMALLEST VALUES

Shows distributions of dataset with lowest and highest limits.

Formula: Range=xmax−xminRange = x_{max} - x_{min}

Variance

VARIANCE = AVERAGE OF THE SQUARED DEVIATIONS FROM THE MEAN

Shows how far the numbers are spread out from their average value.

Formula: σ2=∑i=1n(xi−xˉ)2n\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}

Standard deviation

STANDARD DEVIATION = SQUARE ROOT OF THE VARIANCE

Shows how much variation there is from the mean.

Formula: σ=σ2=∑i=1n(xi−xˉ)2n\sigma = \sqrt{\sigma^2} = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}}

What is Market Research ?

Systematic and objective identification , collection, analysis and interpretation of data to develop marketing strategy or solve a market problem.

  • Allows company to discover target market
  • Links consumer with marketer (marketing decisions)
  • Get feedback/opinion from customers
  • In-house or by third-party companies

Uses

  • Identify market opportunities and problems
  • Evaluate potential market actions
  • Monitor marketing performance
  • Help understand customer behaviour

Tools

  • Surveys (questionnaires, interviews)
  • Product testing
  • Focus groups (observations, experiments)

Types of Research

Basic Research

  • Verify an existing theory or learn more about a concept or phenomenon - Not aimed at solving a particular pragmatic problem

Applied Research

  • Conducted when a decision must be made about a specific real-life problem - Studies are designed to solve practical problems of the modern world

Marketing Research Process

Marketing Research Process Marketing Research Process

Step 1: Identify and define the problem

  • Starts with problem discovery
  • Find something that has gone wrong
  • Gap between what actual and ideal situation (what should have happened and what actually happened)
  • Low grades of students in mathematics - Decrease in company's sales - Preference of mode of transport - High rate of employee turnover - Low wages of workers

Step 2: Set objectives

  • What do you want to achieve?
  • What do you want to learn?
  • What do you want to know?
  • Figuring out the impact of studying hours on grades - Finding the impact of discounts on sales volume - Role of gender in choosing career paths

Research Method

  • Exploratory
  • Descriptive
  • Casual research

"The objectives of the study, the available data sources, the urgency of the decision and the cost of obtaining the data will determine which method should be chosen."

Surveys

  • Most common method of descriptive research
  • data from sample using a questionnaire
  • writing questions, selecting sample, collecting data, analyzing data

Population vs Sample

Population = entire group.


Sample = subset of population. Sampling = process of selecting a subset of population.

Population vs Sample Population vs Sample

For a good sampling we need:

  • who is to be sampled ?
  • how large a sample is needed ?
  • how sampling units will be selected ?

A good sample should have the same characteristics as the population.

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Fundamentals of Statistics

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Data Collection Methods

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What is statistics ?Measures of central tendencyMeanMedianModeMeasures of dispersionRangeVarianceStandard deviationWhat is Market Research ?UsesToolsTypes of ResearchBasic ResearchApplied ResearchMarketing Research ProcessStep 1: Identify and define the problemStep 2: Set objectivesResearch MethodSurveysPopulation vs Sample