Data Handling: Developing Questions

Data Handling

Developing Questions

• Purpose: The first step in the statistical process involves posing questions that justify data collection and guide the data collection process.
• Impact: These questions affect the type of data needed and inform the methods used for data collection, organization, representation, and measurement.

Posing Questions

• Key Concepts:
  • Population: The entire group about which data is being collected.
  • Sample: A smaller subset chosen to represent the population, especially when the population is large and collecting data from the entire population is impractical.
  • Survey: The process of collecting data from a sample (or population).

Considerations of Bias

• Representative Sample: Ensure the sample reflects the same features and characteristics as the population to avoid bias.
• Sample Size: Choose a sample size large enough to provide an accurate reflection of the population.

Data Collection Instruments

• Questionnaire: A document with a list of questions aimed at gathering information about a group or their opinions on a particular topic.
• Recording Sheet: A document used to record the frequency of events, the duration of events, or specific features of events.

Key Steps and Methods

• Pose Relevant Questions:
  • Determine the purpose of the data collection.
  • Formulate specific questions that will guide the type of data to be collected.
• Select the Data Collection Instrument:
  • Choose between a questionnaire or a recording sheet based on the nature of the data and the target population.
• Define the Population and Sample:
  • Identify the population for the data collection.
  • Select a representative sample that reflects the characteristics of the population.
• Design the Data Collection Tool:
  • For a questionnaire, include questions that cover all necessary categories (e.g., age, gender, etc.).
  • For a recording sheet, design it to capture the required information effectively (e.g., number of visitors at different times of the day).
• Ensure Data Collection is Free from Bias:
  • Make sure the sample accurately represents the population.
  • Avoid any factors that might skew the data collection process.
• Collect and Record Data:
  • Use the chosen instrument to gather data from the sample.
  • Ensure accurate and consistent recording of the collected data.

Summarising Data

Measures of Central Tendency: Mean, Median, and Mode

• Mean: The sum of all values in a data set divided by the number of values.
• Median: The middle value in a sorted data set.
• Mode: The value that occurs most frequently in a data set.

Measures of Spread: Range

• Range: The difference between the highest and lowest values in a data set.

Choosing the Appropriate Measure

• Mean: Appropriate when the data set has no extreme outliers and the values are relatively evenly distributed.
• Median: Better when the data set has outliers or is skewed, as it provides a central value without being affected by extremes.
• Mode: Useful for categorical data or when identifying the most common value is important.

Impact of Outliers

• Outliers: Extreme values that differ significantly from other values in the data set.
• Effect on Measures: Outliers can skew the mean, making it unrepresentative of the data.

Steps to Summarise Data

• Calculate the Mean:
  • Add all values together.
  • Divide by the number of values.
• Calculate the Median:
  • Sort the data set.
  • Identify the middle value (or average of two middle values if even number of values).
• Identify the Mode:
  • Determine the most frequently occurring value.
• Calculate the Range:
  • Subtract the lowest value from the highest value.
• Compare the Measures:
  • Assess the mean, median, and mode in the context of the data set.
  • Consider the presence of outliers and their impact.
  • Choose the measure that best represents the data.

Representing, Interpreting and Analysing Data

Types of Graphs and Their Uses

• Double Bar Graphs:
  • Display two bars for each interval, with each bar representing a different category of the data.
  • Height of each bar corresponds to the frequency of a category.
  • Useful for comparing the frequency values for different categories over various intervals.
• Vertical Stack Graphs:
  • Contain two bars for each interval, stacked vertically.
  • Each part of the bar represents a different category within the data (e.g., males and females).
  • Height of each section of the bar equals the frequency values recorded in the frequency table.
  • Useful for showing the total frequency of two combined categories and illustrating the different components making up this total frequency.
• Pie-of-Pie and Bar-of-Pie Charts:
  • Bar-of-Pie Charts: A pie chart that shows a comparison between two different categories of data, with stacked bars showing the components of each category.
  • Pie-of-Pie Charts: Pie charts showing the components of the main categories in a larger pie chart.
  • Useful for comparing the components of different categories and especially when each component comprises more categories.
• Two Line Graphs on the Same Set of Axes:
  • Effective for showing how changes occur in a data set over time, identifying trends.
  • Placing two line graphs on the same set of axes allows for comparing changes in different data sets over time and how they change relative to each other.
• Scatter Plot Graphs:
  • Useful for comparing the type of relationship between two different variables or quantities when no obvious pattern is visible.
  • Constructed by plotting points on a set of axes, with each point representing two different values for the variables or quantities.
  • By observing the scatter of points, one can identify patterns in the relationship between variables and determine the strength of the correlation (weak or strong).

Key Concepts and Terminology

• Correlation: Describes the relationship or pattern between two variables.
• Outliers: Points in the data that deviate significantly from the other points, indicating that while a general pattern may exist, there are instances where it does not hold true.

Key Concepts

• Sorting and Arranging Data:
  • Sorting data involves arranging it in a particular order.
  • For numerical data, this could mean ordering from smallest to largest or vice versa.
  • For categorical data, it could involve arranging alphabetically.
  • Sorting helps in making sense of data by organizing it in a manageable and understandable format.
• Frequency Tables and Tallies:
  • Frequency value indicates how often a particular piece of data appears in a data set.
  • Frequency tables summarize how often different values appear in a data set, allowing for comparisons.
  • Class intervals are used to group large sets of data into more manageable categories.
  • Frequency tables often contain separate columns for different categories (e.g., males and females) and may include percentage values for easier comparison.