STA 111: Introductory Concepts of Statistics
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Questions and Answers

What was the percent of children aged 5-9 in Botswana still at school in 1991?

  • 42.7
  • 49.0 (correct)
  • 50.5
  • 64.7

Which of the following is not a cause of misuse of statistics?

  • Inappropriate sampling methods
  • Selective reporting
  • Bias of the researcher
  • Consulting a statistician (correct)

Which of the following represents descriptive statistics?

  • Evaluation of causal relationships
  • Summarization of population data (correct)
  • Prediction of future trends based on current data
  • Testing a hypothesis for generalizability

In the context of statistics, which of the following is a tool used for graphical representation?

<p>Frequency distribution (C)</p> Signup and view all the answers

What is the primary goal of inferential statistics?

<p>To estimate population parameters (D)</p> Signup and view all the answers

Which of the following data types is frequency and percentage most useful for describing?

<p>Categorical data (A)</p> Signup and view all the answers

Choosing the wrong method for summarizing data can lead to what issue?

<p>Unjustified conclusions (C)</p> Signup and view all the answers

Which method is recommended to reduce statistical misuse before conducting surveys?

<p>Consult a statistician (D)</p> Signup and view all the answers

What is the origin of the term 'statistics'?

<p>It originates from a Latin word meaning state. (C)</p> Signup and view all the answers

Who coined the term 'statistics'?

<p>Gottfried Achenwall (C)</p> Signup and view all the answers

Which of the following best describes statistics as a field of study?

<p>The science of collecting, organizing, and interpreting data. (C)</p> Signup and view all the answers

In which century did the term statistics begin to be associated with data interpretation and making inferences?

<p>19th century (B)</p> Signup and view all the answers

What does the term 'statistic' refer to in its singular form?

<p>A numerical figure or value. (B)</p> Signup and view all the answers

Which of the following is NOT a common way to present numerical facts?

<p>Mathematical equations (D)</p> Signup and view all the answers

During which years did the percentage of children aged 5-9 in Botswana significantly improve in school attendance according to the example?

<p>1981 to 2001 (D)</p> Signup and view all the answers

Why did rulers and kings in the past use statistics?

<p>To assess military potential and wealth. (C)</p> Signup and view all the answers

What is the primary advantage of using the median over the mean when analyzing skewed data?

<p>The median is not sensitive to outliers. (D)</p> Signup and view all the answers

Which statistical measure is used to describe the spread of the data?

<p>Standard deviation (A)</p> Signup and view all the answers

In a symmetrical data distribution, which equality holds true?

<p>Mean = Median = Mode (D)</p> Signup and view all the answers

When reporting data that is skewed, which measures should be used?

<p>Median and IQ Range (A)</p> Signup and view all the answers

Which of the following describes a parameter in statistics?

<p>A summary measure computed from a population (B)</p> Signup and view all the answers

In the provided examples, which represents a sample statistic?

<p>Mean completion time of an assignment for a randomly selected group of 3000 UB students (D)</p> Signup and view all the answers

What does the range of a dataset measure?

<p>The maximum value minus the minimum value (D)</p> Signup and view all the answers

What is a sampling unit in the context of the described exercise?

<p>The section of students from each faculty (A)</p> Signup and view all the answers

What is the main purpose of inferential statistics?

<p>To make general statements about a population based on sample data (D)</p> Signup and view all the answers

Which of the following best describes a population in statistics?

<p>The entire collection of units being studied (C)</p> Signup and view all the answers

What is a sample in statistical terms?

<p>A subset of the population being studied (A)</p> Signup and view all the answers

How does a parameter differ from a statistic?

<p>A parameter summarizes data for the entire population, whereas a statistic summarizes data for a sample (A)</p> Signup and view all the answers

What defines a variable in statistics?

<p>A characteristic that can take on multiple values (C)</p> Signup and view all the answers

Which of the following statements about raw data is correct?

<p>Raw data consists of numerical information in its original form (A)</p> Signup and view all the answers

What is the term for the different values that a variable can assume during observation?

<p>Observations (D)</p> Signup and view all the answers

Which option correctly describes a constant in statistical terms?

<p>A characteristic that is always equal across units (C)</p> Signup and view all the answers

Flashcards

Descriptive Statistics

Summarizes population data by numerically or graphically describing observations in a sample.

Misuse of Statistics

Inappropriate use of statistical methods, data collection, analysis, or conclusions.

Inferential Statistics

Makes predictions or generalizations about a population based on sample data.

Graphical Displays

Visual representations of statistical data, like charts and graphs, to understand patterns and trends.

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Measures of Central Tendency

Describes the center of a data set, such as mean, median, or mode.

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Measures of Variability

Describes how spread out the data is, such as standard deviation and variance.

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Statistical Data

Numerical information collected and analyzed using statistical methods.

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Sampling

Selecting a subset of a population to represent the entire group for research.

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Statistics (singular form)

A number, numerical figure, or value representing data.

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Statistics (field of study)

The science of collecting, organizing, presenting, analyzing, and interpreting data to improve decision-making.

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Origin of Statistics

The term 'statistics' comes from the Latin "status" (or Italian "statista" or German "Statistik"), referring to the state or government.

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Early use of Statistics

Historically, rulers and kings collected data about land, agriculture, commerce, and populations, primarily to assess the state's strength and resources.

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Gottfried Achenwall

A German scholar who coined the term statistics to describe 'collection, processing, and use of data by the state'.

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Presentation of Numerical Facts

Numerical information can be presented using sentences, tables, or graphs.

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Data

Numerical or factual information.

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19th Century Statistics

Statistics became associated with organizing, analyzing, interpreting data, and making inferences from samples about populations.

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Unit

A single member of a group being studied, like a person, animal, or object.

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Population

The complete set of all units of interest in a study.

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Sample

A subset of a population used for study.

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Variable

A characteristic of a unit that can change or take on different values.

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Observation

A value of a variable measured on a unit.

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Raw Data

Unprocessed numerical information collected directly from a source.

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Parameter

A numerical value that describes a population.

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Statistic

A numerical value that summarizes a sample.

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Mean

The average of a dataset. It is calculated by summing all values and dividing by the count.

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Median

The middle value in a sorted dataset. If there are two middle values, it's the average of those.

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Mode

The most frequently occurring value in a dataset.

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Range

The difference between the largest and smallest values in a dataset.

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IQ Range

The difference between the 75th and 25th percentiles in a dataset.

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Standard Deviation

A measure of how spread out numbers are from the mean in a dataset.

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Symmetrical Data

Data that follows a normal distribution where the mean, median, and mode are equal.

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Skewed Data

Data that is not normally distributed, meaning the mean, median, and mode are not equal.

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Study Notes

Course Information

  • Course: STA 111: Elementary Statistics
  • Institution: University of Botswana
  • Department: Department of Statistics

Chapter 1: Introductory Concepts of Statistics

1.1 What is Statistics? - History

  • Origin of the term "statistics" is from Latin "status" or Italian "statista" or German "Statistik", referring to the political state or government.
  • In the past, rulers used statistics for limited applications such as land, agriculture, commerce, populations, military potential, wealth, taxation, and government aspects.
  • The German scholar Gottfried Achenwall coined the term statistics to refer to the "collection, processing, and use of data by the state."
  • In the 19th century, the term "statistics" began to include collection, organizing, analysis, interpretation, and making inferences from sample data about the general population.
  • A reference is provided: https://www.emathzone.com/tutorials/basic-statistics/history-of-statistics.html

1.2 Definition of Statistics

  • Statistics has two definitions:
    • Numerical information (data): In singular form, it is a number, numerical figure, or value.
    • Field of study: The science of collecting, organizing, presenting, analyzing, and interpreting data to aid in effective decision-making.

1.3 Presentation of Numerical Facts

  • Numerical facts can be presented using sentence form, table form, or graphical form.
  • Example (presented as a sentence): In 1981 and 1991, the percentage of children aged 5-9 still at school in Botswana was 42.7% and 49.0% respectively. This improved significantly to 64.7% in 2001.
  • Example (presented as a table): A table is presented showing the percent of children in Botswana aged 5-9 years still at school by census year (1981, 1991, 2001).
  • Graphical representation example: a bar graph is provided illustrating these percentages.

1.4 Applications of Statistics

  • Statistical data and methods are crucial in all fields of human endeavour (social sciences, politics, sports, health, accounting, business, management, history, law, life sciences, etc.).
  • Knowing statistics is essential for acquiring knowledge and achieving success.

1.5 Misuse of Statistics

  • Despite its strengths, statistics can be misused. Examples of misuse are found in Darrell Huff's "How to Lie with Statistics."
  • Causes of misuse arise at various stages of statistical research, including:
    • Inappropriate data collection methods (sampling).
    • Use of unrepresentative subgroups in a study.
    • Inappropriate data summarization methods.
    • Incorrect analysis and inference techniques.
    • Researcher bias
    • Selective reporting or unjustified conclusions.

1.6 Types of Statistics

  • Statistics is broadly categorized into Descriptive and Inferential statistics.
  • Both types are important and use different methods or techniques to achieve different objectives.

1.6.1 Descriptive Statistics

  • Summarizes population data by describing what is observed numerically or graphically in a sample.
  • Descriptive statistics tools include
    • Graphical displays.
    • Measures of central tendency and variability (e.g., mean, standard deviation).
    • Useful tools for categoric data (frequency, percentages)

1.6.2 Inferential Statistics

  • Uses observed data to make statements about the larger population from which the sample was drawn.
  • Includes:
    • Hypothesis testing.
    • Estimation of population characteristics.

1.7 Basic Statistical Concepts

  • Unit: A member of a set of entities being studied (e.g., person, car, animal).
  • Data: Collected through measurement or observation of unit characteristics.
  • Population: The entire collection of individuals/objects relevant to a study.
  • Sample: A subset of the population.
  • Variable: A characteristic of a unit that can take on different values (e.g., shoe size, height, religion).
  • Constant: A characteristic that has the same value for all units.
  • Observation: The specific value/measurement of a variable for a particular unit.
  • Raw Data: Numerical information collected in its original form, unprocessed.
    • Example: The votes received by candidates in an election in Goodhope-Mabule, 15th August, 2015.
  • Parameter: A numerical characteristic summarizing the data for the entire population (e.g., average age).
  • Statistic: A numerical characteristic summarizing the data for the sample (e.g., average age of students in a sample).
  • Symmetrical Data: Data that follows a normal distribution (mean, median, mode are all equal)
  • Skewed Data: Data that is not normally distributed (report median & IQ range).

How to avoid Misusing Statistics

  • Understand elementary course concepts.
  • Consult a statistician for surveys and analysis.

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University of Botswana Statistics Lecture Notes PDF

Description

This quiz covers the foundational concepts of statistics, including its history and development. Explore how statistics evolved from its origins related to governance and its modern applications in data analysis and interpretation. Gain a clearer understanding of what constitutes statistics today.

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