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.</p> Signup and view all the answers

    When is calculating the mean appropriate?

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

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

    <p>Variance</p> Signup and view all the answers

    What kind of variables can the median be used with?

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

    What is the average revenue in 2016?

    <p>24,260 €</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.</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.</p> Signup and view all the answers

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

    <p>Mean</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.</p> Signup and view all the answers

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

    <p>2015</p> Signup and view all the answers

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

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

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

    <p>2018</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.</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.</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.</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'.</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.</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.</p> Signup and view all the answers

    What is a thematic grid primarily used for?

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

    When should the coding function be utilized?

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

    What is an essential step in the coding process?

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

    What is NOT a use of the verbatim function?

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

    What is the mean monthly spending given in the data?

    <p>1132</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</p> Signup and view all the answers

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

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

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

    <p>1</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</p> Signup and view all the answers

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

    <p>2.1</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</p> Signup and view all the answers

    What is the median monthly spending provided in the data?

    <p>1000</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</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    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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    Related Documents

    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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