krit.club logo

Statistics and Probability - Planning and collecting data

Grade 7IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Primary Data: Data collected first-hand by the researcher (e.g., surveys, experiments).

Secondary Data: Data that has already been collected by someone else (e.g., internet, books, government records).

Qualitative Data: Descriptive data that cannot be measured with numbers (e.g., colors, names).

Quantitative Data: Numerical data that can be counted or measured.

Discrete Data: Quantitative data that can only take specific values, usually whole numbers (e.g., number of students).

Continuous Data: Quantitative data that can take any value within a range (e.g., height, weight, time).

Bias: A flaw in data collection that makes the results unrepresentative of the whole population (e.g., asking only your friends for their opinion).

Sample vs Population: A population is the entire group being studied; a sample is a smaller part of the population used for the study.

Tally Charts and Frequency Tables: Tools used to organize and count data systematically.

📐Formulae

Relative Frequency=Frequency of a specific outcomeTotal number of trials/observations\text{Relative Frequency} = \frac{\text{Frequency of a specific outcome}}{\text{Total number of trials/observations}}

Range=Highest ValueLowest Value\text{Range} = \text{Highest Value} - \text{Lowest Value}

Mean=xn (Sum of values ÷ total count)\text{Mean} = \frac{\sum x}{n} \text{ (Sum of values } \div \text{ total count)}

💡Examples

Problem 1:

Classify the following types of data: (a) The number of goals scored in a match, (b) The time taken to run 100 meters, (c) The brand of shoes worn by students.

Solution:

(a) Quantitative - Discrete, (b) Quantitative - Continuous, (c) Qualitative.

Explanation:

Goals are counted in whole numbers (Discrete). Time is measured and can have infinite decimals (Continuous). Shoe brands are descriptive categories (Qualitative).

Problem 2:

A student wants to find out the most popular sport in a school of 1000 pupils. He asks 10 people in the football team. Explain why this sample is biased.

Solution:

The sample is biased because it is too small and not representative of the whole school.

Explanation:

By asking only members of the football team, the student is likely to get an over-representation of people who prefer football. A better method would be a random sample of students from different classes.

Problem 3:

In a survey of 40 people, 12 said their favorite fruit is Apple. Calculate the relative frequency of people who chose Apple.

Solution:

12÷40=0.312 \div 40 = 0.3 or 30%30\%.

Explanation:

Relative frequency is calculated by dividing the frequency of the specific event (12) by the total number of people surveyed (40).

Problem 4:

A researcher wants to know the average height of trees in a forest. Identify if this is Primary or Secondary data if the researcher goes into the forest to measure them himself.

Solution:

Primary Data.

Explanation:

Because the researcher is collecting the measurements first-hand specifically for his own study, it is classified as primary data.