Question

the smaller the standard deviation, the data is ________ concentrated.

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Explanation:

Define standard deviation

Using the Standard Deviation and Measures of Spread knowledge points

$$ \sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2} $$

Analyze the relationship with data concentration

Using the Standard Deviation knowledge point

• A smaller standard deviation means individual data points \(x_i\) are closer to the mean \(\mu\).
• Therefore, the data points are clustered tightly around the center, making the distribution more concentrated.

Answer:

The smaller the standard deviation, the data is * more (Correct answer) concentrated.

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