Mean, Median, Mode

Multiple Choice

Which of the following is a primary reason why statisticians use measures of central tendency?

• To simplify large datasets into single, representative values

• To increase the number of data points in a dataset

• To make data more complex

• To eliminate outliers from the dataset

Open Ended

Explain the difference between mean, median, and mode. When might you choose one measure over the others?

Multiple Choice

Which measure of central tendency is defined as the arithmetic average of all values in a dataset?

• Mean

• Median

• Mode

• Range

Multiple Choice

Based on the example provided, what is the mean of the dataset: 60, 70, 80, 90, 100?

• 80

• 70

• 100

• 60

Multiple Select

Which of the following are strengths of using the mean as a measure of central tendency?

• Uses all data points

• Mathematically precise

• Easy to calculate

• Sensitive to outliers

Open Ended

Describe a situation where using the mean might not accurately represent the center of a dataset. What alternative measure could be more appropriate?

Open Ended

Explain how the calculation of the median differs when there is an even number of values versus an odd number of values in a dataset.

Multiple Choice

Which of the following statements best describes how to find the median in a dataset with an odd number of values?

• Arrange the data in order and select the middle value.

• Add all the values and divide by the number of values.

• Find the value that occurs most frequently.

• Arrange the data in order and select the largest value.

Multiple Choice

What is one major strength of the median compared to other measures of central tendency?

• It is resistant to outliers.

• It uses all data values in its calculation.

• It is always the same as the mean.

• It is the easiest to calculate for large datasets.

Multiple Choice

Based on the examples provided, why might two very different datasets have the same median?

• The median only considers the position of values, not their magnitude.

• The median is always the average of all values.

• The median ignores the order of the data.

• The median is affected by outliers.

Multiple Select

Which of the following are strengths of the mode as a measure of central tendency?

• Works with categorical data

• Easy to identify

• Not affected by outliers

• Requires numerical data

Multiple Choice

Which of the following is a weakness of using the mode as a measure of central tendency?

• It is always unique for any dataset.

• It always represents the center of the data.

• It is unstable in small samples.

• It has more mathematical properties than the mean.

Multiple Select

In which situations is it most appropriate to use the mean, median, or mode? Select all that apply.

• Use the mean when the data is approximately symmetric and has no significant outliers.

• Use the median when the data is skewed or has outliers.

• Use the mode when you want to know the most common value in categorical data.

• Use the mean when you want a resistant measure of center.

Multiple Choice

When comparing symmetric, right skewed, left skewed, and bimodal distributions, which measure tends to remain central regardless of the skew?

• Mean

• Median

• Mode

• Standard deviation

Open Ended

Reflect on a scenario where you would prefer your teacher to use the median instead of the mean for grading. Explain your reasoning.

Open Ended

How do measures of central tendency help us make sense of large datasets?