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Data Handling and Probability - Calculating the Mean, Median, and Mode

Grade 5IGCSE

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

🔑Concepts

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Averages: Mean, Median, and Mode are three different ways to describe the 'center' of a data set.

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Mean: Often called the 'average', it is the sum of all values divided by the total count of values.

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Median: The middle value in a list of numbers that has been sorted from smallest to largest.

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Mode: The value that appears most frequently in a data set. A set can have one mode, more than one mode (bimodal), or no mode.

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Range: The difference between the highest and lowest values, used to measure the spread of the data.

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Data Ordering: Always arrange data in ascending order (smallest to largest) before calculating the median.

📐Formulae

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

Median=The middle value in an ordered list\text{Median} = \text{The middle value in an ordered list}

Mode=The value with the highest frequency\text{Mode} = \text{The value with the highest frequency}

Range=Maximum value−Minimum value\text{Range} = \text{Maximum value} - \text{Minimum value}

💡Examples

Problem 1:

Find the Mean of the following test scores: 7, 8, 5, 10, 10.

Solution:

Mean = 8

Explanation:

Add the scores together: 7+8+5+10+10=407 + 8 + 5 + 10 + 10 = 40. There are 5 scores in total. Divide the sum by the count: 40÷5=840 \div 5 = 8.

Problem 2:

Find the Median of this data set: 12, 4, 15, 7, 9.

Solution:

Median = 9

Explanation:

First, arrange the numbers in order from smallest to largest: 4, 7, 9, 12, 15. The number in the exact middle of this ordered list is 9.

Problem 3:

Identify the Mode and Range for the following list of shoe sizes: 4, 6, 4, 5, 8, 4, 7.

Solution:

Mode = 4, Range = 4

Explanation:

The number 4 appears three times, which is more than any other number, so the Mode is 4. To find the Range, subtract the smallest value (4) from the largest value (8): 8−4=48 - 4 = 4.