Interpreting Standard Deviation

What does standard deviation measure in a dataset?

• The average value of the data points

• The difference between the highest and lowest values

• How spread out the data points are from the mean

• The median value of the dataset

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If a dataset has a high standard deviation, what does it indicate about the data points?

• They are very close to the mean

• They are very spread out from the mean

• All data points are the same

• The dataset cannot be analyzed

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What can be inferred about a dataset with a low standard deviation?

• The data points are randomly distributed

• The data points are spread out over a wide range

• The data points are closely packed to the mean

• The dataset contains no outliers

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In which of the following real-life scenarios would standard deviation be important to understand?

• Deciding what color to paint a room

• Measuring the consistency of temperatures in a city throughout the year

• Choosing a name for a pet

• Planning a one-time event

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If two datasets have the same mean but different standard deviations, what does this tell us?

• They have the same data points

• They have data points spread out in the same way

• One has data points more spread out than the other

• They cannot be compared

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Why is standard deviation considered a better measure of spread than the range of a dataset?

• It only considers the extreme values

• It provides a more detailed picture of the spread

• It is easier to calculate

• It is not affected by outliers

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What does a standard deviation of 0 indicate about a dataset?

• The dataset has no mean

• All data points in the dataset are the same

• The dataset is perfectly normal

• The dataset has no outliers

How does standard deviation relate to the bell curve (normal distribution)?

• It determines the height of the bell curve

• It has no relation to the bell curve

• It determines the width of the bell curve

• It predicts the outliers in the bell curve

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In the context of test scores in a class, what would a high standard deviation indicate?

• All students scored similarly

• The test was too easy

• The test scores varied widely among students

• The test was too difficult

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Which of the following is a true statement about standard deviation?

• It can never be negative

• It decreases as data points become more spread out

• It is the square root of the mean

• It is the same as the mean

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