Statistics: Measures of Central Tendency
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Questions and Answers

What is the mode in a data set?

  • The middle value when data is ordered.
  • The value that appears most frequently in the data set. (correct)
  • The average of all data values.
  • The spread of the data around a central value.

Which measure of central tendency is not apt for quantitative variables?

  • Variance
  • Median
  • Mode (correct)
  • Mean

Which statement accurately defines the mean?

  • A measure that only applies to qualitative variables.
  • A calculated representative value that may not physically exist. (correct)
  • The sum of all values minus one is divided by the count.
  • An arbitrary number chosen to represent the data.

What formula is used to calculate the arithmetic mean?

<p>Sum of values divided by the number of observations. (B)</p> Signup and view all the answers

When is calculating the mean appropriate?

<p>For numeric variables only. (D)</p> Signup and view all the answers

Which measure of central tendency indicates the extent of dispersion in data?

<p>Variance (B)</p> Signup and view all the answers

What kind of variables can the median be used with?

<p>Quantitative variables only. (D)</p> Signup and view all the answers

What characterizes the mode as a measure of central tendency?

<p>It is defined for all variable types, including nominal. (B)</p> Signup and view all the answers

How is variance related to measures of central tendency?

<p>It quantifies the variability or spread of the data around the mean. (D)</p> Signup and view all the answers

Which of the following is true regarding the mean for nominal variables?

<p>The mean cannot be calculated because it does not apply. (C)</p> Signup and view all the answers

What is the average revenue in 2016?

<p>24,260 € (A)</p> Signup and view all the answers

Which statement about the median revenue is true?

<p>It represents the middle point in the revenue distribution. (C)</p> Signup and view all the answers

What can be inferred from the decils mentioned?

<p>Decils are measures that indicate specific percentiles in income distribution. (A)</p> Signup and view all the answers

If data are distributed normally, what should be chosen for analysis?

<p>Mean (B)</p> Signup and view all the answers

When is it more appropriate to use the median instead of the mean?

<p>When data distributions are skewed or contain outliers. (D)</p> Signup and view all the answers

Which year had a median revenue of 20,930 €?

<p>2015 (A)</p> Signup and view all the answers

What percentage of French individuals earn more than 39,130 €?

<p>10% (D)</p> Signup and view all the answers

Which year had the highest average revenue according to the data provided?

<p>2018 (C)</p> Signup and view all the answers

What is the primary purpose of categorizing responses in qualitative analysis?

<p>To assign a category to each answer based on common themes. (A)</p> Signup and view all the answers

What is the first step in building a thematic grid for categorizing responses?

<p>Give a name to your thematic grid. (B)</p> Signup and view all the answers

In what manner should each category be labeled in a thematic grid?

<p>So that it conveys meaningful themes for categorization. (D)</p> Signup and view all the answers

What action should be taken after selecting the appropriate category for a response?

<p>Cut and paste the response as an 'Extract'. (A)</p> Signup and view all the answers

During the coding process, what should you do before moving to the next response?

<p>Save your decision. (D)</p> Signup and view all the answers

Why might one choose to select more than one category for a response?

<p>If the response reflects multiple themes or concepts. (B)</p> Signup and view all the answers

What is a thematic grid primarily used for?

<p>To categorize textual answers based on identified themes. (B)</p> Signup and view all the answers

What is implicit in the need for building a thematic grid?

<p>The complexity of textual responses makes categorization necessary. (D)</p> Signup and view all the answers

What is the primary purpose of the verbatim function in Sphinx?

<p>To provide a direct copy of responses without analysis (A)</p> Signup and view all the answers

When should the coding function be utilized?

<p>To classify responses into predefined categories for further analysis (A)</p> Signup and view all the answers

What type of analysis can be conducted by comparing male and female responses?

<p>Descriptive analysis providing gender-specific insights (D)</p> Signup and view all the answers

Which of the following is a limitation of using the verbatim function?

<p>It is not efficient for analyzing large sets of responses (A)</p> Signup and view all the answers

What is an essential step in the coding process?

<p>Adding categories after assessing the responses (D)</p> Signup and view all the answers

What is NOT a use of the verbatim function?

<p>To analyze patterns across large data sets (B)</p> Signup and view all the answers

What is one benefit of using keyword clouds alongside verbatim analysis?

<p>They visually represent frequently mentioned themes in responses (C)</p> Signup and view all the answers

When conducting analysis by gender, what is an accurate outcome?

<p>It can provide insights specific to particular demographic groups (B)</p> Signup and view all the answers

What is the mean monthly spending given in the data?

<p>1132 (D)</p> Signup and view all the answers

Which of the following options is NOT a method for modifying classes in the analysis?

<p>Random assignment (C)</p> Signup and view all the answers

What is the appropriate format for indicating the upper boundaries of classes?

<p>500;1000;1500;2000 (B)</p> Signup and view all the answers

What is the median time spent on maintenance according to the data?

<p>1 (A)</p> Signup and view all the answers

Which statement correctly reflects how Likert scales are treated in social science?

<p>They are treated as numerical discrete variables (A)</p> Signup and view all the answers

What is the mean time spent on maintenance reported in the content?

<p>2.1 (C)</p> Signup and view all the answers

Which of the following is a suggested approach for class boundaries in analysis?

<p>Indicating upper boundaries only (D)</p> Signup and view all the answers

What is the median monthly spending provided in the data?

<p>1000 (B)</p> Signup and view all the answers

For the purpose of analysis, what type of variable is a Likert scale considered to be?

<p>Ordinal categorical variable (A)</p> Signup and view all the answers

Which of the following best describes what Sphinx automatically creates during analysis?

<p>Classes for variables (A)</p> Signup and view all the answers

What is the first step in the textual analysis process with open-ended survey responses?

<p>Identification of concepts (D)</p> Signup and view all the answers

Which tool is used to synthesize information in categorical form during textual analysis?

<p>Codification tool (B)</p> Signup and view all the answers

When utilizing keyword clouds in textual analysis, what kind of responses are best suited for a single-word answer?

<p>Open-ended questions (B)</p> Signup and view all the answers

What visual representation is highlighted in keyword clouds during textual analysis?

<p>Most frequently appearing words (D)</p> Signup and view all the answers

In Sphinx, which type of variables appears when analyzing textual questions?

<p>Text variables indicated by the 'ab' icon (A)</p> Signup and view all the answers

How can keyword clouds provide comparative insight according to participant sub-groups?

<p>By dividing samples based on demographic variables (D)</p> Signup and view all the answers

Which step follows the identification of themes in the textual analysis process?

<p>Codification of themes (A)</p> Signup and view all the answers

What is a keyword cloud primarily used for in textual analysis?

<p>Highlighting response similarities (D)</p> Signup and view all the answers

What should a researcher do to analyze textual responses in Sphinx?

<p>Choose the 'Textual Analysis' option (A)</p> Signup and view all the answers

What type of variable can be created using the codification process in textual analysis?

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

Flashcards

Central Tendency

The central tendency is a measure that describes the typical value of a dataset. It shows where the data points tend to cluster around a central point.

Mode

The mode is the value that appears most frequently in a dataset. It's useful for understanding the most common outcome in a set of data.

Mean

The mean is the average of a dataset. It's calculated by summing up all the values and dividing by the number of values. It provides a representative value for the entire dataset.

Median

The median is the middle value in a dataset when the values are arranged in order. It divides the dataset into two equal halves.

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Variance or Dispersion

The variance or dispersion measures how spread out the data points are from the mean. A high variance indicates a wider spread, while a low variance indicates a tighter cluster.

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Arithmetic Mean

The arithmetic mean is a specific type of mean calculation that involves adding all the values and dividing by the number of values. It's the most common type of mean used in statistical analysis.

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Open-Ended Questions

Open-ended questions are questions that allow respondents to provide their own answers, rather than being limited to pre-defined options. These questions generate numeric variables, which can be used in calculations like the mean.

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Numeric Variables

Numeric Variables are variables that represent numerical values. They can be measured and quantified, allowing for calculations like the mean.

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Nominal Variables

Nominal variables are variables that represent categories or labels. They don't have a numerical order or value.

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Mean as a Representative Value

The mean is not a real value in the dataset. It's a calculated value that represents the average of the data points.

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Average Revenue

The average revenue is the sum of all revenues divided by the number of data points. It gives an overall measure of revenue.

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Deciles

Deciles divide a dataset into 10 equal parts, each representing 10% of the data. They help understand the distribution of data across different income levels.

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When to use Median

If your data has extreme values (outliers) that significantly distort the overall average, the median is a better measure of central tendency than the mean. The median remains unaffected by extreme values.

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When to use Mean

If your data is normally distributed (bell-shaped), the mean is a better measure of central tendency. It represents the typical value in the dataset.

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Median Advantage

The median is the preferred measure when you are interested in the middle value of the dataset, regardless of the influence of extreme values.

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Mean Advantage

The mean is the preferred measure when you want to use the average value to represent the typical value in a dataset. It provides a good overall measure.

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What are Classes in Sphinx?

Classes are categories into which data is grouped in Sphinx.

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How to Create Classes in Sphinx?

You can select from different methods to create classes, such as "Of the same value" or "Around the mean."

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Personalized Classes in Sphinx

The "Personalized" class creation option lets you specify the exact upper bounds for each category.

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Why Modify Classes in Sphinx?

Sphinx automatically creates classes based on a default setting but sometimes you need to change them to fit your analysis.

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Use Classes in Sphinx

In Sphinx, the "Use Classes" button allows you to determine how you want to group your data into classes.

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Likert Scales as Numerical Data

Likert scales are often treated as numerical variables in social sciences, allowing for the calculation of a mean.

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Changing Likert Scales in Sphinx

Sphinx defaults Likert scales as ordinal variables, but you need to change them to discrete continuous variables for proper analysis.

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Use Classes for Data Analysis

The "Use Classes" feature in Sphinx helps analyze data by grouping it into meaningful categories for the analysis.

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Sphinx for Meaningful Analysis

Sphinx provides tools and options to make your analysis meaningful. By changing classes and settings, you gain insights from your data.

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What is the 'Verbatim' function in Sphinx?

This function presents all responses "word for word", without any analysis. Useful for finding specific answers or quotes.

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What is the 'Coding' function in Sphinx?

This function classifies responses into categories, requiring analysis and categorization of each response.

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What is a Keyword Cloud?

It shows a visual representation of the most common words or phrases in a dataset.

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What is 'Analysis by Contexts'?

This analysis looks at the responses of specific groups within a dataset, allowing for a deeper understanding of their individual characteristics.

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When is the 'Verbatim' function useful?

Often used with open-ended questions that require a sentence or more as an answer.

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How can you use 'Verbatim' with Keyword Clouds?

It's helpful when you need to identify possible categories for coding responses.

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Describe the steps involved in coding.

It involves looking at the responses, identifying categories, going through all responses assigning categories, and finally adding new categories if needed.

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Why is 'Analysis by Contexts' important?

It allows researchers to identify patterns and insights within specific groups that might not be apparent in the overall dataset.

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Textual Analysis

A technique used to analyze textual data from surveys by identifying common themes, creating categories, and coding each observation. It allows researchers to understand the underlying meaning and trends in open-ended responses.

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Keyword Cloud

A visual representation of words that appear most often in textual data. The size of each word reflects its frequency. Helps identify important themes and concepts within text.

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Codification

The process of assigning each observation (e.g., survey response) to a predefined category. This transforms textual data into numerical data for analysis.

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Keyword Cloud by Context

A feature on Sphinx that allows you to create multiple keyword clouds based on different sub-groups within your sample. This helps compare themes across different demographics.

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Textual Analysis on Sphinx

The ability to analyze textual data for open-ended questions on Sphinx. It allows you to create keyword clouds, view verbatim responses, and apply codification for detailed analysis.

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Benefits of Textual Analysis

Using Sphinx to analyze open-ended questions allows you to create keyword clouds, view individual responses, and categorize them into themes. This helps uncover trends and understanding the data, going beyond just numerical values.

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Codification Tool

A tool used by Sphinx to synthesize textual data by creating categorical variables. It helps researchers turn open-ended responses into quantifiable data.

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Verbatim

A tool that allows you to analyze individual survey responses in their original form. This helps understand the context and richness of the data.

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Keyword Cloud Customization

Sphinx allows you to create multiple keyword clouds, breaking your sample into different groups based on specific variables. This lets you compare the differences in themes and opinions across different demographic groups.

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Comparative Textual Analysis

You can analyze the same open-ended questions for different sub-groups of your sample, such as men vs. women. This helps you understand the differences in how people respond to the same prompts.

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Categorizing responses

The process of grouping similar responses together based on common themes or concepts.

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Thematic grid

A structured framework used to categorize responses in a systematic manner.

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Theme

A label that describes a specific category within a thematic grid.

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Coding responses

The process of assigning a specific category or theme to each response based on its content.

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Extract

Text from a survey response that is deemed representative of a specific category in the thematic grid.

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Grouping data into classes (Sphinx)

A way of interpreting responses by grouping them into pre-defined categories. This allows for analysis of trends and patterns across groups.

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Modifying classes (Sphinx)

The ability to adjust class boundaries in Sphinx to best capture the specific nuances of the data.

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Using classes for analysis (Sphinx)

The process of analyzing data by considering the grouping of data into classes, rather than just individual values.

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Study Notes

Univariate Descriptive Statistics and Textual Analysis

  • Univariate descriptive statistics are used to analyze data points from one variable at a time
  • Measures of central tendency describe the typical or central value in a dataset
  • Central tendency measures the extent to which data values cluster around a typical or central value.
  • Four main measures of central tendency include mode, mean, median, and variance/dispersion.
  • Mode is the outcome with the highest frequency in qualitative variables.
  • Mean is the calculated average of all observed values in a sample.
  • Mean is calculated by adding all observed values and dividing by the number of observations.
  • Mean is suitable for quantitative variables but not for nominal data
  • Median is the middle value separating the higher half from the lower half of a dataset.
  • Median is less influenced by extreme values compared to the mean
  • Example of using mean- mean size of households in France(2015)=2.23 people.
  • Example of variables where mean can be use- How old are you?, What is your monthly income?, How much did you pay for your car?,Likert scale questions.
  • Example of brands and unit sales- Levi's(259), Diesel(209), Guess(145), Energie(120), Gap(94), Pepe Jeans(76), Calvin Klein(61), Dolce&Gabbana(48), Armani(43)
  • Frequency table is not usually created when there are a large number of outcomes.
  • In Sphinx, variables identified with a symbol 74 represent numerical variables.

Mode

  • Mode represents the most frequent value in a dataset.
  • Mode is only applicable for qualitative variables.

Mean

  • Mean is the average of all values in a dataset.
  • Mean is sensitive to extreme values in a dataset.
  • Mean is calculated by summing up all the values and dividing by the total count of values

Median

  • Median is the middle value when the dataset is arranged numerically.
  • Median is less sensitive to extreme values compared to the mean

Example

  • Average revenue is systematically higher than the median revenue

Why Using the Mean?

  • The number of outcomes is usually too large to create a frequency table
  • This table has many items having only 1 or 2 respondents
  • Mean is used for analyzing variables with numerical data, including open-ended questions where the answer is a number

In Sphinx

  • For the analysis, click on 'Open Sphinx', open the 'Automobiles survey', check on "Go to Analysis" module and click on 'Go back to the analysis standard environment.'
  • Click 'New Analysis' and select the 'Age of the car' variable to retrieve its frequency table and pie chart

Analysis of the Variable

  • Sphinx automatically generates 'classes'. This is sometimes needed to manually adjust variables for greater meaning.
  • Example statistics of analysis of a variable: Mean, Median, Standard deviation, Range
  • For the 'Age of car' example; 87.5% of data points had the value 'Yes', while 12.5% had the value 'No'

Advantages/Disadvantages of Using Means

  • Mean is easily understood by most people but using it can result in extreme values influencing calculations significantly.
  • The wider the spread from the mean value, the more difficult it will be to analyze the distribution.
  • The mean and median are helpful for describing a dataset in a succinct way.

Median

  • Median is a useful statistic when there are extreme values in a dataset.
  • Median divides the data to two equal parts
  • Median is less sensitive to extreme values in a dataset

When to Use The Mean?

  • If the data is normally distributed, use the mean.
  • If the dataset has extreme values, use the median.
  • Check the nature of the data to determine an appropriate measure
  • The mean is calculated by dividing the sum of the values in the dataset by the number of values in the sample

Calculating the Mean

  • The mean (x) is calculated by adding all observed outcomes (Xi) and dividing by the number of observations (n): x= ∑ Xi / n

Numerical Variables

  • Numerical variables are commonly analyzed by presenting their descriptive statistics.
  • In some cases, variables can be converted into ordinal variables by creating classes

Part II: Textual analysis

  • Open-ended questions can generate textual variables, where outcomes consist of words, ideas, or sentences
  • Sphinx provides tools to analyze both numerical and textual variables

What is Textual Analysis?

  • Textual analysis is a method to transform textual data into categorical nominal variables
  • Frequency of presence of certain topic or content can be counted within the survey
  • Frequencies of textual data in nominal categories help in estimating frequencies and percentages
  • Textual analysis can be used to identify themes and patterns
  • Data analysts can identify recurring concepts or themes

The Textual Analysis Process

  • Identifying concepts/themes/categories frequently appearing in answers to survey questions
  • This involves identifying common themes or concepts from a sample of survey participants
  • Creating categories or themes to classify the recurring answers
  • Codifying survey participant responses based on identified categories

The Textual Analysis Process on Sphinx

  • Use keyword clouds to summarize the data
  • Using Sphinx's coding tool to develop categorical variables from the data
  • Display the categorical variable results

Textual Analysis on Sphinx

  • Use the 'Keywords Clouds', 'Verbatim', and 'Codification' functions for analysis of open-ended questions on surveys.
  • Open survey, access 'Analysis'
  • Click on 'New analysis', and select 'Textual analysis' to perform textual analysis

Adding a Category

  • Modify the thematic grid using a pencil icon

End of Coding

  • End of coding creates a new variable based on the thematic grid name (e.g. Ideal Car)
  • This variable is a categorical variable and can be analyzed

Analysis by Context

  • Sphinx allows for creating keyword clouds grouped by specific variables (e.g. men vs. women)
  • By context, you can compare the keyword clouds of differing subgroups (e.g., men and women) within the same test group.

Coding Function

  • Important coding function classifies responses into categories
  • Each response is analyzed and categorized using predefined themes or categories, or a newly created one to accurately reflect the sentiment or topics discussed by survey participants/respondents, etc.

Steps in Coding

  • Review survey results for common themes and concepts
  • Create categories or themes to classify the responses
  • Review all responses and categorize them with the predefined themes from step 2 (adding to/modifying these during this process is acceptable)
  • Add new categories if required to ensure all responses are categorized accurately.

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Univariate Descriptive Statistics & Textual Analysis PDF

Description

Test your knowledge on measures of central tendency, including the mean, median, and mode. This quiz covers key concepts, formulas, and appropriateness of each measure in various contexts. Perfect for students studying statistics or data analysis.

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