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Statistics and Data - Finding the mode and the mean of a data set

Grade 4IGCSE

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

🔑Concepts

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A data set is a collection of numbers or information gathered from observations or experiments.

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The Mode is the value that appears most frequently in a data set. It is the 'most popular' number.

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A data set can have one mode, more than one mode (bimodal), or no mode at all if all numbers appear the same number of times.

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The Mean is the 'average' of the data. It is calculated by sharing the total sum equally among the number of items in the set.

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The Mean provides a single value that represents the central point of the data.

📐Formulae

Mean=Sum of all valuesTotal number of values\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}

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

💡Examples

Problem 1:

Find the mode and the mean of the following data set: 5, 8, 3, 5, 4.

Solution:

Mode = 5; Mean = 5

Explanation:

To find the mode, identify the number that appears most often. 5 appears twice, while the others appear once. To find the mean, add all the numbers: 5+8+3+5+4=255 + 8 + 3 + 5 + 4 = 25. Then divide the sum by the number of values (5): 25÷5=525 \div 5 = 5.

Problem 2:

A student records the temperature for four days: 12∘C12^\circ C, 15∘C15^\circ C, 18∘C18^\circ C, and 15∘C15^\circ C. Calculate the mean temperature.

Solution:

15∘C15^\circ C

Explanation:

First, find the sum of the temperatures: 12+15+18+15=6012 + 15 + 18 + 15 = 60. There are 4 days of data. Divide the sum by the number of days: 60÷4=1560 \div 4 = 15.

Problem 3:

Determine the mode for the following list of shoe sizes: 4, 6, 4, 7, 6, 8.

Solution:

4 and 6

Explanation:

In this data set, both the number 4 and the number 6 appear exactly twice. Since they both have the highest frequency, the data set is bimodal, meaning it has two modes: 4 and 6.