Data Handling and Probability - Creating frequency tables and bar charts

Grade 5IGCSE

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

🔑Concepts

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Data Collection: The process of gathering information by observing, asking questions, or measuring.

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Tally Marks: A quick way of recording data in groups of five (four vertical lines crossed by a diagonal fifth line).

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

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Frequency Table: A table used to organize data showing categories, tallies, and the final frequency count.

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Bar Chart: A visual display of data using rectangular bars where the height (or length) represents the frequency.

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Axes Labeling: The horizontal axis (x-axis) usually shows categories, and the vertical axis (y-axis) shows the frequency/scale.

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Discrete Data: Data that can only take certain values (e.g., number of students, shoe sizes) - bar charts for discrete data must have gaps between bars.

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Scaling: Choosing an appropriate interval for the y-axis (e.g., counting by 1s, 2s, 5s, or 10s) based on the highest frequency.

📐Formulae

\text{Total Frequency} = \sum \text{individual frequencies}

\text{Probability of an event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

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

💡Examples

Problem 1:

A class of 20 students was asked about their favorite pets. The results were: Cat, Dog, Cat, Fish, Dog, Dog, Rabbit, Cat, Dog, Fish, Cat, Dog, Rabbit, Dog, Cat, Dog, Cat, Fish, Dog, Cat. Create a frequency table.

Solution:

Pet: Cat | Tally: |||| || | Frequency: 7 Pet: Dog | Tally: |||| ||| | Frequency: 8 Pet: Fish | Tally: ||| | Frequency: 3 Pet: Rabbit | Tally: || | Frequency: 2 Total: 20

Explanation:

List each unique pet type. For every occurrence in the raw data, place a tally mark. Group tallies in 5s for easy counting. Sum the tallies to find the frequency for each category.

Problem 2:

Using the pet data (Cat: 7, Dog: 8, Fish: 3, Rabbit: 2), what scale should you use for the y-axis of a bar chart and why?

Solution:

A scale of 1 unit per grid line (0, 1, 2, 3, 4, 5, 6, 7, 8).

Explanation:

Since the highest frequency is 8, a scale of 1 is the most precise and easiest to read. If the frequencies were much higher (e.g., 80), a scale of 10 would be more appropriate.

Problem 3:

From the pet frequency table, what is the probability that a student chosen at random prefers a Dog? Write as a fraction.

Solution:

\frac{8}{20}

Explanation:

Probability is calculated by taking the frequency of the specific outcome (8 students like dogs) and dividing it by the total number of outcomes (20 students in total).