L3.2: Describing Numerical Data - Mean

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Learning outcomes

• define arithmetic mean
• compute mean from raw data
• explain what mean represents
• recognize when mean can be misleading

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What is the mean?

• The arithmetic mean is the average value.

• mean = sum of observations / number of observations

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Example

• 4, 6, 8, 10, 12

• sum = 40
• number of observations = 5
• mean = 40/5 = 8

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What the mean tells us

• Mean is a measure of central tendency.
• It gives the balancing point of the data.

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Mean and outliers

• Mean is affected by extreme values.

• 5, 5, 6, 6, 100

• (5 + 5 + 6 + 6 + 100) / 5 = 24.4

• 24.4 does not represent the typical value well here because 100 is an outlier.

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When mean is useful

• when data are numerical
• when all values are relevant to the summary
• when extreme values are not distorting interpretation too much

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Exam hints and traps

• Mean uses all observations.
• Mean can be decimal even if all observations are whole numbers.
• Mean is not always one of the observed values.
• Do not use mean for nominal categorical data.

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Quick practice

1. Find the mean of 3, 5, 7, 9.
2. Find the mean of 10, 10, 10, 20.
3. Explain why mean may be weak for 1, 1, 2, 50.

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Answer key

1. (3 + 5 + 7 + 9)/4 = 6
2. 50/4 = 12.5
3. Because the extreme value 50 pulls the average upward.