STATISTICS FUNDAMENTALS
Study Notes • Formulas • Examples • Revision Questions • MCQs
1. What Is Statistics?
Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data. It helps summarize information,
identify patterns, compare groups, and make evidence-based decisions.
Example: A teacher can calculate the average of a class's test scores to summarize performance.
2. Population and Sample
• Population: The complete group a study wants to understand.
• Sample: A smaller part of the population selected for study.
• Census: Data collection from every member of a population.
• Sampling: Selecting members to represent a population.
Example: If a college has 2,000 students and a researcher surveys 150, all 2,000 are the population and the 150 surveyed
students are the sample.
3. Types of Data
• Qualitative: Categories or qualities, such as eye colour or transport type.
• Quantitative: Numerical values, such as age, height, or test score.
• Discrete: Countable values, often whole numbers, such as number of books.
• Continuous: Measured values that can take any value within a range, such as time or temperature.
4. Descriptive and Inferential Statistics
Descriptive statistics organize and summarize collected data using measures, tables, and graphs.
Inferential statistics use sample data to estimate or draw conclusions about a wider population while accounting for
uncertainty.
5. Measures of Central Tendency
Mean: Add all values and divide by the number of values. Example: (2 + 4 + 6 + 8) / 4 = 5.
Median: The middle value after sorting. For an even number of values, average the two middle values. Example: median of 3, 5,
7 is 5.
Mode: The value that occurs most often. A dataset may have one mode, multiple modes, or no mode.
6. Measures of Spread
Range: Maximum value minus minimum value. Example: for 3, 5, 8, range = 8 − 3 = 5.
Variance: A measure of spread around the mean, based on squared deviations.
Standard deviation: The square root of variance, expressed in the same units as the data. A larger value generally means
more spread.
7. Basic Probability
Probability measures how likely an event is. It ranges from 0 (impossible) to 1 (certain).
For equally likely outcomes: P(event) = favourable outcomes ÷ total possible outcomes.
Example: For a fair six-sided die, P(rolling a 2) = 1/6. Complement rule: P(not A) = 1 − P(A).
8. Sampling Methods
• Simple random: Each population member has an equal chance of selection.
• Systematic: Select every kth member after a random starting point.
• Stratified: Divide the population into groups and sample from each group.
Statistics Fundamentals — Study Notes Page 1
Study Notes • Formulas • Examples • Revision Questions • MCQs
1. What Is Statistics?
Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data. It helps summarize information,
identify patterns, compare groups, and make evidence-based decisions.
Example: A teacher can calculate the average of a class's test scores to summarize performance.
2. Population and Sample
• Population: The complete group a study wants to understand.
• Sample: A smaller part of the population selected for study.
• Census: Data collection from every member of a population.
• Sampling: Selecting members to represent a population.
Example: If a college has 2,000 students and a researcher surveys 150, all 2,000 are the population and the 150 surveyed
students are the sample.
3. Types of Data
• Qualitative: Categories or qualities, such as eye colour or transport type.
• Quantitative: Numerical values, such as age, height, or test score.
• Discrete: Countable values, often whole numbers, such as number of books.
• Continuous: Measured values that can take any value within a range, such as time or temperature.
4. Descriptive and Inferential Statistics
Descriptive statistics organize and summarize collected data using measures, tables, and graphs.
Inferential statistics use sample data to estimate or draw conclusions about a wider population while accounting for
uncertainty.
5. Measures of Central Tendency
Mean: Add all values and divide by the number of values. Example: (2 + 4 + 6 + 8) / 4 = 5.
Median: The middle value after sorting. For an even number of values, average the two middle values. Example: median of 3, 5,
7 is 5.
Mode: The value that occurs most often. A dataset may have one mode, multiple modes, or no mode.
6. Measures of Spread
Range: Maximum value minus minimum value. Example: for 3, 5, 8, range = 8 − 3 = 5.
Variance: A measure of spread around the mean, based on squared deviations.
Standard deviation: The square root of variance, expressed in the same units as the data. A larger value generally means
more spread.
7. Basic Probability
Probability measures how likely an event is. It ranges from 0 (impossible) to 1 (certain).
For equally likely outcomes: P(event) = favourable outcomes ÷ total possible outcomes.
Example: For a fair six-sided die, P(rolling a 2) = 1/6. Complement rule: P(not A) = 1 − P(A).
8. Sampling Methods
• Simple random: Each population member has an equal chance of selection.
• Systematic: Select every kth member after a random starting point.
• Stratified: Divide the population into groups and sample from each group.
Statistics Fundamentals — Study Notes Page 1
