variance and standard deviation

Which of the following best describes the standard deviation of a dataset?

• It is the difference between the highest and lowest scores.

• It is the average of all the data values.

• It measures how spread out the data values are around the mean.

• It measures the frequency of each data point.

Variance of a dataset is defined as:

• The cube of the mean.

• The standard deviation multiplied by the mean.

• The average of the squared deviations from the mean.

• The difference between the median and the mode.

You have recorded the height of every student in your school. To calculate variance:

• Use the sample variance formula, dividing by n−1

• Use the population variance formula, dividing by n

• It doesn’t matter which formula you use.

• Use neither; height data cannot have a variance

Which statement best distinguishes grouped from ungrouped data?

• Ungrouped data is always numerical; grouped data is always categorical.

• Grouped data has been organized into class intervals with associated frequencies; ungrouped data is in its raw form.

• Ungrouped data must be qualitative; grouped data must be quantitative.

• There is no difference; both terms mean the same thing.

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What is the Number of the correct answer?

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In a grouped frequency table, the representative value used for each class in variance and standard deviation calculations is typically:

• The class boundary.

• The class midpoint.

• The median of the entire dataset.

• The mode of the entire dataset.

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If a dataset’s standard deviation is very large, it implies:

• The data values are closely clustered around the mean.

• The data values are widely spread out from the mean.

• All values in the dataset are identical.

• The mean of the dataset is very small.