Statistics and Probability - Data collection and frequency tables

Grade 6IGCSE

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

🔑Concepts

•

Data Collection: The process of gathering information (data) to answer questions or test hypotheses.

•

Discrete Data: Data that can only take specific values (e.g., number of students, shoe sizes).

•

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

•

Primary Data: Data collected first-hand by the researcher for a specific purpose.

•

Secondary Data: Data collected by someone else previously (e.g., internet, newspapers).

•

Tally Marks: A quick way of recording data in groups of five (IIII with a diagonal strike through) to avoid counting errors.

•

Frequency: The number of times a particular value or category occurs in a data set.

•

Frequency Table: A table used to organize data by listing categories/values alongside their corresponding frequencies.

•

Grouped Frequency Table: Used for large sets of data where values are grouped into 'classes' or 'intervals' (e.g., 0-9, 10-19).

📐Formulae

\text{Total Frequency} = \sum f

\text{Range} = \text{Maximum Value} - \text{Minimum Value}

\text{Relative Frequency} = \frac{\text{Frequency of a category}}{\text{Total Frequency}}

💡Examples

Problem 1:

A group of 15 students were asked how many siblings they have. The results were: 1, 0, 2, 1, 3, 1, 0, 1, 2, 1, 0, 2, 4, 1, 2. Create a frequency table for this data.

Solution:

Siblings Tally Frequency 0 III 3 1 IIII I 6 2 IIII 4 3 I 1 4 I 1 Total 15

Explanation:

First, list the unique values (0, 1, 2, 3, 4). Go through the raw data and place a tally mark for each occurrence. Finally, count the tallies to find the frequency for each number of siblings. Ensure the sum of frequencies equals the total number of students (15).

Problem 2:

The heights (in cm) of 10 plants are: 12, 15, 22, 28, 14, 25, 18, 29, 21, 11. Organize this data into a grouped frequency table with class intervals of 10-19, 20-29.

Solution:

Height (cm) Tally Frequency 10 - 19 IIIII 5 20 - 29 IIIII 5 Total 10

Explanation:

Identify which values fall into the 10-19 range (12, 15, 14, 18, 11) and which fall into the 20-29 range (22, 28, 25, 29, 21). Grouping data makes it easier to manage when there are many different individual values.

Problem 3:

In a frequency table, the 'Total Frequency' is 40. If the frequency of 'Red cars' is 8, what is the relative frequency of Red cars?

Solution:

\text{Relative Frequency} = \frac{8}{40} = \frac{1}{5} = 0.2

Explanation:

Relative frequency compares the frequency of a specific category to the total. It can be expressed as a fraction, decimal, or percentage.