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Statistics and Probability - Calculating mean, median, mode, and range

Grade 6IGCSE

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

🔑Concepts

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Mean: The average of a data set, found by adding all numbers and dividing by the count.

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Median: The middle value in a list of numbers ordered 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/multimodal), or no mode.

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Range: The difference between the highest and lowest values, representing the spread of the data.

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Ordering Data: To find the median and range accurately, always arrange the data in ascending order first.

📐Formulae

Mean=∑xn=Sum of all valuesTotal number of values\text{Mean} = \frac{\sum x}{n} = \frac{\text{Sum of all values}}{\text{Total number of values}}

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

Median Position=n+12th value (in an ordered list)\text{Median Position} = \frac{n + 1}{2} \text{th value (in an ordered list)}

💡Examples

Problem 1:

Find the mean, median, mode, and range for the following test scores: 12, 15, 12, 10, 18, 20, 15, 12.

Solution:

Sorted Data: 10, 12, 12, 12, 15, 15, 18, 20.

  1. Mean: (10+12+12+12+15+15+18+20) / 8 = 114 / 8 = 14.25.
  2. Median: Average of 4th and 5th values: (12 + 15) / 2 = 13.5.
  3. Mode: 12 (appears three times).
  4. Range: 20 - 10 = 10.

Explanation:

First, sort the data. The mean is the total sum divided by 8. Since there is an even number of values (8), the median is the average of the two middle numbers. The mode is the most frequent number, and the range is the gap between the highest and lowest score.

Problem 2:

The heights of five plants in cm are: 5, 8, 4, 10, 3. Calculate the range and mean height.

Solution:

  1. Range: 10 - 3 = 7 cm.
  2. Mean: (5 + 8 + 4 + 10 + 3) / 5 = 30 / 5 = 6 cm.

Explanation:

The range identifies the spread of growth (7 cm). The mean provides the average height of the plants (6 cm) by distributing the total height equally across the five plants.