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• Study notes on data handling, developing questions, classifying and organising data, summarising data, and representing, interpreting, and analysing data.

Developing Questions

• Research questions can be open-ended or closed.

Open-ended Questions

• Allow respondents to answer in their own words, providing unbiased data and detailed, qualitative insights.
• They can be time-consuming to answer and analyse, and respondents may skip them if they take too long.

Closed Questions

• Provide predefined options for respondents to choose from, making them convenient and quick to answer.
• They are easier to analyse and compare responses.
• They may not accommodate all respondents' views, leading to incomplete answers.

Collecting Data

• Data collection is influenced by the research aim, population, and sample.
• Population is the entire group from which data is collected.
• Sample is a subset of the population chosen to represent it.
• Sample bias occurs when the sample does not accurately represent the population.
• Random sampling can minimize bias.

Methods of Collecting Data

• Observation, questionnaires, and interviews are all methods of collecting data.

Observation

• Data collection by watching and recording results without interacting with people.
• Avoids interaction biases and is useful for collecting behavioural data.
• Limited to observable phenomena and does not capture respondents' attitudes or opinions.

Questionnaire

• A list of questions given to respondents to collect data directly from them.
• Anonymity can encourage honesty making it suitable for large samples.
• Responses may be limited by the questions' design and lacks the ability to probe deeper into responses.

Interview

• An interviewer asks questions and records the responses.
• It can clarify ambiguous answers and probe for more detailed information.
• Time-consuming and may introduce interviewer bias.

Classifying and Organising Data

• Organising data involves arranging information into a specific order i.e. ascending or descending to make it easier to read and analyse
• Classifying data involves grouping data into classes based on a common feature to simplify the data for better understanding and analysis
• Tally marks are used to count how many items fall into each category in an efficient and visually intuitive manner

Using Tally Marks

• Use vertical lines to represent counts.
• Every fifth count is represented by a line crossing the previous four, making it easier to count by fives and quickly assess the totals.

Frequency Tables

• Displays the frequency of various outcomes in a sample
• Shows 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). It organizes the data into specified ranges, helping to identify patterns or trends.

Measures of Central Tendency

• Mean, median, and mode are measures of central tendency.

Mean

• The sum of all the values divided by the number of values.
• Provides a single value that represents the central point of the data set.
• Calculated as:

$$Mean = \frac{\text{Sum of all values}}{\text{Number of values}}$$

Median

• The middle value in a data set when the values are arranged in ascending or descending order.
• Less affected by outliers and skewed data than the mean.
• To calculate, arrange the data in order and find the middle value; if there is an even number of values, the median is the average of the two middle values.

Mode

• The value that appears most frequently in the data set.
• Useful for categorical data where we want to know the most common category.
• Identify the value that occurs most often; if no value repeats, there is no mode.

Measures of Spread

• Range, quartiles, interquartile range (IQR), and percentiles are measures of spread.

Range

• The difference between the highest and lowest values in the data set.
• Provides a measure of how spread out the values are.
• Calculated as:

$$Range = \text{Highest value} - \text{Lowest value}$$

Quartiles

• Divide the data set into four equal parts.
• Help understand the spread and distribution of the data.
• To calculate, arrange the data in order, divide it into four equal parts; the lower quartile (Q1) is the median of the lower half, the median (Q2) is the overall median, and the upper quartile (Q3) is the median of the upper half.

Interquartile Range (IQR)

• The range of the middle 50% of the data.
• Measures the spread of the central portion of the data, which is less affected by outliers.
• Calculated as:

$$IQR = Q3 - Q1$$

Percentiles

• Divide the data set into 100 equal parts.
• Used to understand the distribution of data and compare individual values to the entire data set.
• Identify the value below which a given percentage of the data falls.

Purposes of Graphs

• Graphs are used to visually represent data for various purposes: for exploring relationships, displaying and reporting and for identifying patterns
• Graphs must highlight key findings, show the relationships, and properly label axes with the dependent variable on the vertical or y axis and the independent variable on the horizontal or x axis

Types of Graphs

• Line graphs, bar graphs, histograms, scatter plots, pie charts, and box and whisker plots.

Line Graphs

• Show the relationship between two quantities over time with Data points connected by straight lines.

Bar Graphs

• represent data sorted into categories Bars show the number of items in each category, with spaces between the bars.
• Types: Single, double, multiple, compound, or stacked bar graphs.

Histograms

• Represent continuous data grouped into ranges.
• Bars touch each other, indicating continuous data.

Scatter Plots

• Used to study the relationship between two variables.
• Each point represents a pair of values, showing patterns of correlation (positive, negative, or none).

Pie Charts

• Show parts of a whole.
• Circular graph divided into sectors, representing percentages that add up to 100%.

Box and Whisker Plots

• Summarize data using the five-number summary (minimum, Q1, median, Q3, maximum).
• A box showing the interquartile range and whiskers extending to the minimum and maximum values.

Interpreting and Analysing Graphs

• Line graphs show trends and changes over time and are useful for observing increases or decreases.
• Bar graphs compare different categories allowing comparisons to which category is the largest or smallest.
• Histograms show the distribution of continuous data and are useful for identifying the shape of the data distribution.
• Scatter plots identify correlations between two variables with patterns indicate the type of correlation.
• Pie charts compare parts of a whole and are useful for showing relative sizes of categories.
• Box and whisker plots summarize data distributions and are useful for identifying outliers and spread.