Mean

Definition

The mean is the average of a set of numbers, calculated by dividing the sum of all values by the number of values. It is a measure of central tendency in a data set.

5 Must Know Facts For Your Next Test

1. The formula for the mean is $\bar{x} = \frac{\sum x_i}{n}$, where $\sum x_i$ is the sum of all values and $n$ is the number of values.
2. The mean is sensitive to outliers, which can skew the results significantly.
3. In a normal distribution, the mean, median, and mode are all equal.
4. The sample mean can be used to estimate the population mean when using random sampling.
5. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as sample size increases.

Review Questions

• What is the formula for calculating the mean?
• How does an outlier affect the mean?
• According to the Central Limit Theorem, what happens to the sampling distribution of the sample mean as sample size increases?

Related terms

Median:

The median is the middle value in a data set when it is ordered from least to greatest. If there are an even number of observations, it is the average of the two middle numbers.

Mode:

The mode is the value that appears most frequently in a data set. A data set may have one mode, more than one mode, or no mode at all.

Standard Deviation:

Standard deviation measures how spread out numbers are around their mean. It quantifies variability or dispersion in a data set.