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Statistics and Probability - Interpreting and discussing results

Grade 7IGCSE

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

🔑Concepts

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Comparing datasets using measures of central tendency (Mean, Median, Mode) to describe the 'average' or 'typical' value.

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Using the Range to describe the spread or consistency of data; a smaller range indicates more consistent results.

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Identifying and discussing outliers—values that are significantly higher or lower than the rest of the data—and their impact on the mean.

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Interpreting trends and patterns from statistical diagrams such as bar charts, pie charts, and line graphs.

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Comparing experimental probability (relative frequency) with theoretical probability, noting that results often get closer to theoretical values as the number of trials increases.

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Drawing conclusions about a population based on a sample while considering potential bias.

📐Formulae

Mean=∑xn\text{Mean} = \frac{\sum x}{n} (Sum of values divided by the number of values)

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

Relative Frequency=Frequency of eventTotal number of trials\text{Relative Frequency} = \frac{\text{Frequency of event}}{\text{Total number of trials}}

Probability of an event P(E)=Number of favorable outcomesTotal number of possible outcomes\text{Probability of an event } P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

💡Examples

Problem 1:

Class A has test scores: 15, 16, 17, 18, 19. Class B has test scores: 10, 15, 17, 19, 24. Both have a mean of 17. Which class is more consistent?

Solution:

Class A is more consistent.

Explanation:

To check consistency, we calculate the range. Range A = 19−15=419 - 15 = 4. Range B = 24−10=1424 - 10 = 14. Since Class A has a much smaller range, the scores are closer to the mean and therefore more consistent.

Problem 2:

A set of data is: 4, 5, 5, 6, 7, 35. Which measure of central tendency (Mean or Median) best represents this data?

Solution:

The Median.

Explanation:

The value 35 is an outlier. The mean is 4+5+5+6+7+356=10.33\frac{4+5+5+6+7+35}{6} = 10.33, which is higher than 5 out of the 6 values. The median is 5.5. The median is a better representation because it is not affected by the extreme outlier.

Problem 3:

A coin is flipped 50 times and lands on Heads 30 times. What is the relative frequency of landing on Heads, and how does it compare to the theoretical probability?

Solution:

Relative Frequency = 0.6; Theoretical Probability = 0.5.

Explanation:

The relative frequency is 3050=0.6\frac{30}{50} = 0.6. The theoretical probability of a fair coin is 0.50.5. The difference occurs due to chance in a small sample; if we flipped the coin 1000 times, we would expect the relative frequency to move closer to 0.5.