Statistics and Probability - Correlation, qualitative handling

Grade 10IB

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

🔑Concepts

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x

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(x, y)

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x

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x

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No Correlation: There is no apparent relationship between the variables; the points are scattered randomly on the diagram.

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Strength of Correlation: Described qualitatively as 'Strong' (points are very close to a straight line), 'Moderate', or 'Weak' (points are widely spread but still show a trend).

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(\bar{x}, \bar{y})

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x

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Interpolation and Extrapolation: Interpolation is making a prediction within the range of the given data; Extrapolation is making a prediction outside the range of data, which is generally less reliable.

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Outliers: Data points that lie significantly far away from the general trend of the rest of the data.

📐Formulae

\bar{x} = \frac{\sum x}{n}

\bar{y} = \frac{\sum y}{n}

y = mx + c

m = \frac{y_2 - y_1}{x_2 - x_1}

💡Examples

Problem 1:

x

Solution:

x

Explanation:

(170, 40)

Problem 2:

Describe the correlation if a scatter plot shows that as the outside temperature increases, the sales of hot chocolate decrease, and the points are very close to a straight line.

Solution:

The correlation is Strong Negative Correlation .

Explanation:

It is 'Negative' because as one variable increases, the other decreases. It is 'Strong' because the points lie very close to a straight line.

Problem 3:

y = 0.5x + 10

Solution:

x = 15

Explanation:

y