Basic Statistical Concept

Which of the following best describes the mean of a dataset?

• The value that occurs most frequently in the dataset

• The middle value when the data is arranged in order

• The sum of all data values divided by the number of values

• The difference between the highest and lowest values

The median is preferred over the mean in cases where the dataset is:

• Symmetrical with no outliers

• Uniformly distributed

• Skewed with outliers

• Consisting of nominal data

Answer explanation

• The median is the middle value of an ordered dataset and is less affected by extreme values or outliers. In skewed distributions with outliers, the median provides a better central tendency measure than the mean.

Which of the following scenarios is most appropriate for using the mode as a measure of central tendency?

• Calculating the average age of students in a class

• Determining the most common shoe size sold in a store

• Finding the middle salary in a company's pay scale

• Computing the average test score

Answer explanation

• The mode is the value that appears most frequently in a dataset. It's particularly useful for categorical or discrete data where you're interested in the most common category or value, such as shoe sizes.

Which of the following best describes variance?

• The square root of the standard deviation

• The average of the squared differences from the mean

• The difference between the highest and lowest values

• The middle value of an ordered dataset

Answer explanation

• Variance measures how much the data points in a dataset vary from the mean. It is calculated by taking the average of the squared differences between each data point and the mean.

A small standard deviation in a dataset indicates that:

• The data points are widely spread around the mean

• The data points are closely clustered around the mean

• There are significant outliers in the data

• The data is skewed to the right

Answer explanation

• A small standard deviation means that the data points are close to the mean, indicating low variability in the dataset.

• It suggests consistency among the data values.

According to the Empirical Rule, approximately what percentage of data in a normal distribution falls within two standard deviations of the mean?

• 68%

• 75%

• 95%

• 99.7%

Calculate the standard deviation of the dataset {4,4,4,4}

• 0

• 1

• 2

• Cannot be determined

Which statement about standard deviation is true?

• Standard deviation can never be zero

• Standard deviation is always expressed in the same units as the original data

• Standard deviation is not affected by outliers

• Standard deviation is the square of the variance

Answer explanation

• The standard deviation is the square root of the variance and is measured in the same units as the original data.

• It provides a measure of the average distance of data points from the mean.

Which statement is true regarding the normal distribution and standard deviation?

• Approximately 68% of data falls within one standard deviation in any distribution

• In a normal distribution, about 99.7% of data falls within three standard deviations of the mean

• The Empirical Rule applies to all types of data distributions

• The mean, median, and mode are always different in a normal distribution

Answer explanation

• The Empirical Rule specifically applies to normal distributions and states that approximately 99.7% of data falls within three standard deviations of the mean.

• In a perfectly normal distribution, the mean, median, and mode are all equal.