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Statistics and Probability - Statistical measures (Mean, Median, Mode, Range)

Grade 7IGCSE

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

🔑Concepts

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Mean: The arithmetic average of a data set.

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Median: The middle value when the data is arranged in ascending or descending order.

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Mode: The value that appears most frequently in a data set.

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

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

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Frequency: How many times a particular value occurs in a data set.

📐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}}

Median Position=n+12-th term (where n is the number of data points)\text{Median Position} = \frac{n + 1}{2}\text{-th term (where } n \text{ is the number of data points)}

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

Mean from Frequency Table=∑(fx)∑f\text{Mean from Frequency Table} = \frac{\sum (fx)}{\sum f}

💡Examples

Problem 1:

Find the mean, median, mode, and range for the following data set: 5, 8, 3, 5, 9, 2, 10.

Solution:

Mean = 6, Median = 5, Mode = 5, Range = 8

Explanation:

  1. Mean: (5+8+3+5+9+2+10)/7=42/7=6(5+8+3+5+9+2+10) / 7 = 42 / 7 = 6. 2. Median: Arrange in order: 2, 3, 5, 5, 8, 9, 10. The 4th term is 5. 3. Mode: The number 5 appears twice, more than any other number. 4. Range: 10−2=810 - 2 = 8.

Problem 2:

A set of five numbers has a mean of 12. Four of the numbers are 10, 14, 8, and 15. Find the fifth number.

Solution:

13

Explanation:

Let the fifth number be xx. Total sum = Mean×n=12×5=60\text{Mean} \times n = 12 \times 5 = 60. Sum of known numbers = 10+14+8+15=4710 + 14 + 8 + 15 = 47. Therefore, x=60−47=13x = 60 - 47 = 13.

Problem 3:

Find the mean of the data given in this frequency table: Score (x): 1, 2, 3; Frequency (f): 3, 5, 2.

Solution:

1.9

Explanation:

Total sum ∑(fx)=(1×3)+(2×5)+(3×2)=3+10+6=19\sum(fx) = (1 \times 3) + (2 \times 5) + (3 \times 2) = 3 + 10 + 6 = 19. Total frequency ∑f=3+5+2=10\sum f = 3 + 5 + 2 = 10. Mean=19/10=1.9\text{Mean} = 19 / 10 = 1.9.