Measures of Center and Variability

Learn arithmetic mean, range.

Lesson 2 of 32 parts Practice Flashcards

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Arithmetic Mean

Objective: Explain arithmetic mean, apply the stated method, and check its conditions.

The arithmetic mean is the sum of numerical observations divided by their count. It uses every value and can be shifted by an outlier. A mean need not be an observed value, and it should be reported in the same units as the data. An extreme value can pull the mean away from most observations.

Formulas

$x̄=(Σxᵢ)/n$

Worked examples

Try itFind the mean of 1, 7, and 13.Show answer

Step 1: Add the three observations: 21. Step 2: Divide by the number of observations, 3. Step 3: The mean is 7.

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Arithmetic Mean

Objective: Explain arithmetic mean, apply the stated method, and check its conditions.

Formulas

$x̄=(Σxᵢ)/n$

Worked examples

Try itFind the mean of 1, 7, and 13.Show answer

Step 1: Add the three observations: 21. Step 2: Divide by the number of observations, 3. Step 3: The mean is 7.

Range

Objective: Explain range, apply the stated method, and check its conditions.

The range of a numerical dataset is its maximum minus its minimum. It measures total span but uses only two observations, so it is sensitive to extremes. It does not describe how values are distributed within that span. Equal ranges do not imply identical distributions.

Formulas

$Range = maximum − minimum$

Worked examples

Try itFind the range of 1, 7, and 13.Show answer

Step 1: Range equals maximum minus minimum. Step 2: Compute (13)−(1). Step 3: The range is 12.

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