STATISTICS and PROBABILITY

Which of the following statements is TRUE about variance and what it measures?

• Variance measures the central tendency of a dataset.

• Variance measures the spread of data points around the mean.

• Variance is always a negative value.

• A higher variance means the data points are closer to the mean.

Which of the following statements is NOT true about standard deviation?

• Standard deviation measures the dispersion of data points around the mean.

• A higher standard deviation indicates that data points are more spread out.

• Standard deviation can never be negative.

• Standard deviation is unaffected by outliers in the dataset.

What does a higher variance indicate about the data points?

• They are closer to the mean.

• They are more spread out.

• They are all identical.

• They are skewed to one side.

What does a lower variance indicate?

• Data points are more spread out.

• Data points are random.

• Data points are closer to the mean.

• Data points are unpredictable.

If a dataset has a smaller standard deviation, what does this mean?

• The data points are farther from the mean.

• The dataset has outliers.

• The data points are closer to the mean.

• The dataset has a higher variance.

A larger standard deviation means:

• The data points are very close together.

• The data points are more spread out.

• The mean is lower.

• The data is perfectly symmetrical.

Which of the following statements is FALSE about Standard Error of Mean?

• A smaller SEM means the sample mean is a more accurate estimate of the population mean.

• A larger SEM indicates greater variability and less precision in estimating the population mean.

• Increasing the sample size increases the SEM, making the estimate less reliable.

• Increasing the sample size reduces the SEM, making the estimate more reliable.

Which of the following statements about the Coefficient of Variation is INCORRECT?

• A lower CV indicates more consistency in the data.

• A higher CV means the data points are more spread out relative to the mean.

• CV is not useful for comparing datasets with different units.

• CV helps measure relative variability instead of absolute variability.

If the standard deviation of a data set is 4.45, what is its variance?

• 19.79

• 19.80

• 19.81

• 19.82

If the standard deviation of a data set is 3.87, what is its variance (round off to two decimal places)?

• 14.95

• 14.96

• 14.97

• 14.98