Module 2: Review of Basic Statistics and Hypothesis Testing

What is the primary purpose of descriptive statistics?

• To make inferences about a population from a sample.
• To summarize and describe the main features of a data set.
• To test hypotheses about relationships between variables.
• To determine cause-and-effect relationships.

Answer explanation

Descriptive statistics are used to organize, summarize, and describe characteristics of a data set, such as frequencies, percentages, and measures of central tendency and dispersion.

Which of the following is considered a measure of central tendency?

• Standard Deviation
• Range
• Mode
• Variance

Answer explanation

Measures of central tendency, such as the mean, median, and mode, describe the center point or typical value of a data set. The mode represents the most frequently occurring value.

The mean is best defined as:

• The middle value in a sorted data set.
• The most frequently occurring value in a data set.
• The sum of all values divided by the number of values.
• The difference between the highest and lowest values.

Answer explanation

The mean is calculated by summing all the values in a data set and dividing by the total number of values. It is the most common measure of central tendency.

In a data set, the median is described as the:

• Average of all scores.
• Most common score.
• Middle score when the data are arranged in order of magnitude.
• Difference between the highest and lowest scores.

Answer explanation

The median is the value that separates the higher half from the lower half of a data sample. It is the middle value when the data are ordered from smallest to largest.

When is the mode the most appropriate measure of central tendency to use?

• When the data are normally distributed.
• When the data are nominal or categorical.
• When the data have extreme outliers.
• When precise calculations are required.

Answer explanation

The mode is particularly useful for nominal or categorical data because it identifies the most frequent category or value. It can be used for any level of measurement but is most appropriate when other measures like the mean or median are not suitable.

Which measure of central tendency is least affected by extreme scores (outliers)?

• Mean
• Median
• Mode
• Range

Answer explanation

The median is less sensitive to extreme values than the mean because it is based on the position of values rather than their sum.

What does a measure of dispersion indicate about a data set?

• Its central point.
• The most frequent value.
• The spread or variability of the data.
• The relationship between two variables.

Answer explanation

Measures of dispersion, such as range, variance, and standard deviation, describe how spread out or varied the data points are from the central value.

The range of a data set is calculated by:

• Subtracting the lowest value from the highest value.
• Adding the highest and lowest values.
• Dividing the sum of all values by the number of values.
• Finding the square root of the variance.

Answer explanation

The range is the simplest measure of dispersion and is found by subtracting the minimum value from the maximum value in a data set.

What does the standard deviation represent?

• The average squared difference from the mean.
• The spread of data points around the mean.
• The middle value of the data set.
• The most frequent observation.

Answer explanation

The standard deviation is a measure of the average amount of variability or spread around the mean in a data set. A larger standard deviation indicates greater variability.

A small standard deviation relative to the mean suggests that the data points are:

• Widely dispersed.
• Clustered closely around the mean.
• Bimodal.
• Highly skewed.

Answer explanation

A small standard deviation means that the individual data points are generally close to the mean, indicating low variability and a tight clustering of data.