Mean

Lesson

The mean is the average of a set of numbers, calculated by adding all the numbers in the dataset and dividing by the total number of values. It is useful for understanding the overall trend of a dataset.

Practice Question #1

What is the mean of the following dataset: 2, 4, 6, 8, 10?

A) 4

B) 6

C) 5

D) 7

Select an option above to see an explanation here.

A) B) C) D) undefined

Terms

Mean:: The average of a set of numbers, calculated by adding all the numbers in the dataset and dividing by the total number of values.

Practice Question #2

Which of the following is NOT a measure of central tendency?

A) Mean

B) Median

C) Mode

D) Range

Select an option above to see an explanation here.

A) The mean is a measure of central tendency, as it represents the average value of a dataset. B) The median is a measure of central tendency, as it represents the middle value of a dataset. C) The mode is a measure of central tendency, as it represents the most frequently occurring value in a dataset. D) The range is not a measure of central tendency, as it represents the difference between a dataset's highest and lowest values.

Do Not Confuse With

Range:: The difference between a dataset's highest and lowest values.
Median:: The middle value in a dataset when the values are arranged in ascending or descending order.
Mode:: The value that occurs most frequently in a dataset.
Variance:: A measure of how much the values in a dataset differ from the mean.
Standard Deviation:: The square root of the variance measures the average distance between each value and the mean.

Practice Question #3

Calculate the mean of the following data points: 2, 4, 6, 8, 10

A) 4

B) 5

C) 6

D) 7

Select an option above to see an explanation here.

A) Incorrect. The mean is not the lowest value in the data set. B) Correct. The mean is calculated as (2+4+6+8+10)/5 = 30/5 = 5. C) Incorrect. The mean is not the middle value in the data set. D) Incorrect. The mean is not the highest value in the data set.

Historical Example

In the early 20th century, a famous statistician named Sir Francis Galton conducted a study on the heights of parents and their children. He found that the mean height of the children was closer to the overall mean height of the population than the mean height of their parents. This phenomenon, known as regression to the mean, has been observed in various fields, including finance and economics.

Practice Question #4

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Real-World Example

Suppose a financial analyst wants to calculate the mean return of a stock over the past five years. They gather the annual returns for each year, which are 10%, 15%, 5%, -2%, and 8%. To calculate the mean return, they add all the returns (10 + 15 + 5 - 2 + 8 = 36) and divide by the total number of years (5), resulting in a mean return of 7.2%.

Practice Question #5

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Formulas to Remember

Mean = (Sum of all data points) / (Number of data points)

Practice Question #6

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Formula Examples

Calculate the mean of the following data points: 5, 10, 15, 20, 25 1. Add all the data points: 5 + 10 + 15 + 20 + 25 = 75 2. Count the number of data points: 5 3. Divide the sum by the number of data points: 75 / 5 = 15 The mean of the data points is 15.

Practice Question #7

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Pitfalls to Remember

Outliers:: The mean can be heavily influenced by extreme values (outliers) in the data set, which may not accurately represent the central tendency of the data.
Non-normal distribution:: The mean may not be the best measure of central tendency for data sets with a non-normal distribution (e.g., skewed data).