Statistical Terms, Origins, and Units

Statistical Terms and Origins

• The term "statistics" was first used in 1749.
• Statistics is both a science and an art.
• Statistics aids in business, economic analysis, and administration, covering a wide range of applications.

Jobs of Statistics

• Statistics assists in data classification.
• It helps with hypothesis testing and identifying trends.

Derivation of "Statistics"

• The word "statistics" originates from the German word "Statistik."

Statistical Investigation Considerations

• Key considerations include problem definition, investigation purpose, and information sources.

Simple vs. Composite Units

• A rate of rupees per kilogram is a composite unit, involving two simple units.
• Simple units are single characteristics measured independently (e.g., kg, cm).
• Composite units combine multiple simple units.

Statistical Investigation Objectives

• The objectives are determined before data compilation.

Sampling Definitions

• A sample refers to a part of a population chosen for study.
• Sample size is the number of individuals selected in a sample.

Data Collection Methods

• A census involves surveying every unit related to the study problem. It is called complete enumeration.
• Sample involves selecting a portion of a population.
• The choice depends on the type of investigation.

Essential Elements of a Sample

• Representativeness, independence, and homogeneity are essential.
• Additional requirements include adequacy, similarity, and regularity.

Sample Investigation Laws

• The Law of Statistical Regularity and the Law of Inertia of Large Numbers are related to sample investigation.
• The Law of Statistical Regularity posits that a randomly selected sample should represent the population.
• The Law of Inertia of Large Numbers suggests that larger sample sizes yield more accurate results. Also known as: Principle of stability of mass data.

Sampling Techniques

• Non-random sampling includes quota and convenience sampling.
• Systematic sampling is a type of random sampling.

Random Sampling

• A lottery system is used in random sampling.

Stratified Random Sampling

• Involves dividing a heterogeneous group into homogeneous subgroups and then randomly sampling from each.

Data Processing

• Data transformed through organization, classification, tabulation, and computation is processed data.
• Data collected and left untouched are raw data.

Statistical Investigation Roles

• An enumerator helps the investigator in data collection, by asking question directly and filling the schedule.

Questionnaire Design

• The number of questions in a questionnaire depends on the survey's needs.

Primary Data Collection

• Data collected for the first time by the investigator.

Secondary Data Collection

• Secondary sources involve data that is already published (e.g., docuemnts from application alies/ researches ect).
• Methods: Using observation, interviews, questionnaires.

Sampling Frame

• A list of all units in a population is called a sampling frame.

Data Collection: Snowball Sampling

• Snowball sampling makes use of connecting relations.

Approximation

• Approximation can be achieved by adding to figures, discarding figures, or rounding to the nearest figure.

Sampling Errors

• Sampling errors can arise due to faulty tools, in-adqeuacy of medicine and manipulation. Includes the wrong interpreation of data.

Types of Errors

• Unbiased errors occur accidentally. *Compensating error; accidental or random error.
• Biased errors are systematic or intentional. *Systematic, constant, or cumulative
• Non-sampling errors can be due to non-response, and errors of publication.
• Sampling errors mainly occur during data collection.

Measures of Error

• Absolute error = Actual Value - Estimated Value
• Relative error = Absolute Error / Actual Value
• Percentage error = (Relative Error) * 100

Averages and Statistics

• Boddington stated "Statistics is the science of averages."

Mathematical vs. Positional Averages

• Mean, geometric mean, and harmonic mean are mathematical averages.
• Mode is an average of position.

Averages of Position

• Median, partition values, and mode are positional averages.

Statistical Measures

• Mode is the average of position. With the equal interval of each class size.

Graphical Data

• Arithmetic mean cannot be obtained by graphical methods.

Limitations of the Mode

• An uncommon data set may be difficult to analyise. Other disadvatnges are: A data set may have no mode or Multiple modes

Median Calculation Steps

• The first step in calculating the median is to arrange the data.

Assumptions with Grouped Data

• When computing the mean from grouped data, the assumption is that every value in the class is equal to the midpoint.

Mode Calculation Formula

• Mode = 3 Median - 2 Mean

Effect of Extreme Values

• The arithmetic mean is most affected by extreme values.
• The Median is a most useful average for qualitative facts.

Suitable Averages

• Mode is a suitable average for the size of ready-made garments.

Grouping Method

• Grouping method is used in mode determination.

Calculating Median

• Data needs to be sorted in ascending order for median calculation.

Meanings of Statistical Terms

• The Mid Value of 50 + 60 is 55

Stability of Averages

• Mode average is most unstable in averages because the data is uncertain, unreliable and not correct.

Definition of a Median

• Median is the mid value.

Mode Definition

• Mode is value with maximal frequency. This is used for the "most frequent value of something.

Series of Values

• If all number of value in a series are the same value, then weighted mean is not possible.

Percentiles for the Median

• The median should lie in the 50th percentile.

Analysis

• Data is placed in order of increasing or decreasing for analysis of: "Central Tendancy".