# Mean

The **mean** is a number that shows the center of the data. Another word for *mean* is **average** and it is mathematically symbolized as x̄ (x-bar). However, when calculating the mean of the whole population, you use the Greek letter μ (mu) instead.

To calculate the *average* of a **sample**, you sum all the observations, then divide by the number of observations (n). The formula changes slightly for **population **average. The formulas are below:

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Where:

- Σ(x) represents the total sum of the observations.
- n/N represents the number of observations.

# Median

The **median** of a set of numbers arranged in order of magnitude is the middle value of an *odd number* of measurements, or the mean of the two middle values of an *even number* of measurements. Median is symbolized as x̃ (x-tilda) or with a capital M.

Question:Find the median of the following data: 574 635 645 695 736 746 794 894

Solution:The numbers are in ascending order (always make sure they’re arranged inorder of magnitude). There are an even number of observations (n = 8), therefore you take the average value of observation 4 and 5. null

If you’re still confused, two more examples are demonstrated below.

# Mode

The **mode** of a set of numbers is the value(s) that occurs most often in the set.

- The set: 1 3 3 5 6 7 7 7 9 →
**7** - The set: 1 1 3 3 5 5 7 7 →
**1, 3, 5,**and**7** - The set: 1 3 3 3 5 6 7 7 7 9 →
**3**and**7**

More details on finding the mode can be found in this video.

# Mid-range

The **mid-range** is simply the value midway between the two extreme values, such as the **range**.

The mid-range for the values 3, 5, 6, 6, 7, 11, 11, 15 is: null

Let’s review how to calculate the **mean**, **median**, and **mode **with 2 sample problems.