Questions and Answers
What is the primary advantage of using closed questions in data collection?
What can occur when a sample does not accurately represent the population?
What is the purpose of controlling for demographic factors in sampling?
What type of question allows respondents to answer in their own words?
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What is a limitation of using observation as a method of data collection?
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What is the primary disadvantage of using open-ended questions in data collection?
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What is the purpose of a questionnaire in data collection?
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What influences the choice of the sample and the data collection method?
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What is the main purpose of a line graph?
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What is the formula to calculate the IQR?
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What is the main purpose of a histogram?
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What is the main advantage of using anonymity in data collection?
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What is the primary purpose of classifying data?
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What is the median of a dataset with an even number of values?
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What is the purpose of a box and whisker plot?
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What is the main purpose of using tally marks?
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What is the main purpose of frequency tables?
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What is the definition of a percentile?
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What is the purpose of a scatter plot?
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What is the definition of the mean in statistics?
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What is the main purpose of a bar graph?
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What is the main use of the median in statistics?
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What is the formula to calculate the mean?
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What is the main use of the mode in statistics?
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What is the purpose of the range in a dataset?
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What is the definition of the range in statistics?
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What is the purpose of quartiles in statistics?
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What is the purpose of organising data?
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Study Notes
Developing Research Questions
- Open-ended questions allow respondents to answer in their own words, providing insightful and qualitative data.
- Advantages of open-ended questions: can yield detailed and qualitative insights.
- Disadvantages of open-ended questions: may be time-consuming to answer and analyze, and respondents might skip them if they take too long to answer.
- Closed questions provide predefined options for respondents to choose from, making it convenient and quick to answer.
- Advantages of closed questions: easier to analyze and compare responses.
- Disadvantages of closed questions: may not accommodate all respondents' views, leading to incomplete answers.
Collecting Data
- The research aim influences the choice of the sample and the data collection method.
- Population: the entire group from which data is collected (e.g., Gauteng Matric learners).
- Sample: a subset of the population chosen to represent it (e.g., learners from 10 schools in Gauteng).
- Sample bias: occurs when the sample does not accurately represent the population.
- Solution to sample bias: use random sampling to minimize bias, but still control for demographic factors such as race, gender, and age.
Methods of Collecting Data
- Observation: collecting data by watching and recording results without interacting with people.
- Advantages of observation: avoids interaction biases, useful for collecting behavioral data.
- Disadvantages of observation: limited to observable phenomena, does not capture respondents' attitudes or opinions.
- Questionnaire: a list of questions given to respondents to collect data directly from them.
- Advantages of questionnaire: anonymity can encourage honesty, suitable for large samples.
- Disadvantages of questionnaire: responses may be limited by the questions' design, lacks the ability to probe deeper into responses.
- Interview: an interviewer asks questions and records the responses.
- Advantages of interview: can clarify ambiguous answers, probe for more detailed information.
- Disadvantages of interview: time-consuming, may introduce interviewer bias.
Classifying and Organising Data
Organising Data
- Definition: arranging information into a specific order, such as ascending or descending order.
- Purpose: to make data easier to read and analyze by structuring it systematically.
Classifying Data
- Definition: grouping data into classes based on a common feature.
- Purpose: to simplify the data for better understanding and analysis by categorizing it into relevant groups.
Using Tally Marks
- Purpose: to count how many items fall into each category in an efficient and visually intuitive manner.
- Method: use vertical lines to represent counts, every fifth count is represented by a line crossing the previous four.
Frequency Tables
- Definition: a table that displays the frequency of various outcomes in a sample.
- Purpose: to show how often each category or group appears in the data set.
- Grouped Frequency Table: used for continuous data divided into intervals (e.g., height ranges).
Key Points to Remember
- Organising data helps to arrange information in a clear and systematic manner, facilitating easier reading and analysis.
- Classifying data involves grouping data based on shared characteristics, making it easier to handle and interpret large data sets.
- Tally marks are useful for counting discrete data quickly and efficiently.
- Frequency tables provide a clear summary of how often different values or ranges of values occur in a data set, making it easier to see the distribution and identify patterns.
Summarising Data
Measures of Central Tendency
- Mean (average): the sum of all values divided by the number of values.
- Use: provides a single value that represents the central point of the data set.
- Calculation: add all the values together and divide by the number of values.
- Median: the middle value in a data set when the values are arranged in ascending or descending order.
- Use: is less affected by outliers and skewed data than the mean.
- Calculation: arrange the data in order and find the middle value.
- Mode: the value that appears most frequently in the data set.
- Use: is useful for categorical data where we want to know the most common category.
- Calculation: identify the value that occurs most often.
Measures of Spread
- Range: the difference between the highest and lowest values in the data set.
- Use: provides a measure of how spread out the values are.
- Calculation: subtract the smallest value from the largest value.
- Quartiles: divide the data set into four equal parts.
- Use: help understand the spread and distribution of the data.
- Calculation: arrange the data in order, divide it into four equal parts.
- Interquartile Range (IQR): the range of the middle 50% of the data.
- Use: measures the spread of the central portion of the data.
- Calculation: subtract Q1 from Q3 (IQR = Q3 - Q1).
- Percentiles: divide the data set into 100 equal parts.
- Use: are used to understand the distribution of data and compare individual values to the entire data set.
- Calculation: identify the value below which a given percentage of the data falls.
Representing, Interpreting, and Analysing Data
Purposes of Graphs
- Graphs are used to visually represent data for various purposes, including:
- Exploring relationships
- Displaying and reporting
- Identifying patterns
Types of Graphs
- Line Graphs: show the relationship between two quantities over time.
- Features: data points connected by straight lines.
- Use: show trends and changes over time.
- Bar Graphs: represent data sorted into categories.
- Features: bars show the number of items in each category, with spaces between the bars.
- Use: compare different categories.
- Histograms: represent continuous data grouped into ranges.
- Features: bars touch each other, indicating continuous data.
- Use: show the distribution of continuous data.
- Scatter Plots: study the relationship between two variables.
- Features: each point represents a pair of values, showing patterns of correlation.
- Use: identify correlations between two variables.
- Pie Charts: show parts of a whole.
- Features: circular graph divided into sectors, representing percentages that add up to 100%.
- Use: compare parts of a whole.
- Box and Whisker Plots: summarize data distributions.
- Features: a box showing the interquartile range and whiskers extending to the minimum and maximum values.
- Use: summarize data distributions and identify outliers and spread.
Interpreting and Analysing Graphs
- Identify trends and changes over time in line graphs.
- Compare different categories in bar graphs.
- Identify the distribution of continuous data in histograms.
- Identify correlations between two variables in scatter plots.
- Compare parts of a whole in pie charts.
- Summarize data distributions and identify outliers and spread in box and whisker plots.
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Description
Learn about the different types of research questions, including open-ended and closed questions, and their advantages and disadvantages in data handling.