• The sum of the numbers divided by the number of numbers.
• Also called the ‘Arithmetic Mean’ or Average
• The formula is: [latex]\bar{x} = \frac{\sum_{i=1}^{n} X_i }{n}[/latex]

Understanding Summation Notation (Σ)

• Σ means the summation (to add up all of the x terms).
• It is often used in Statistics
• Many metrics require us to sum up the values or squared values of a data set
• And it is quicker to use the ‘summation notation’ to express that sum.

EXAMPLE 1.1 — USING SUMMATION NOTATION

If the data set ‘X’ contains the following data:

x₁ = 55, x₂ = 62, x₃ = 67, x₄ = 60, x₅ = 71, x₆ = 66

then:

Σ x_i = x₁ + x₂ + x₃ + x₄ + x₅ + x₆

= 55 + 62 + 67 + 60 + 71 + 66

= 381

Calculating Mean Values by Hand (Exercise)

To calculate an average (mean), we simply do the following:

1. Sum up all of the values (Σ x_i)
2. Count the number of values in the data set (n)
3. Divide the sum of all the terms by the number of data in the data set (Σ x_i / n)

Calculating the MEAN USing Excel (Video)

We will use the average call in Excel:

• Type: ‘ = average()’
• Select all of the elements across the row or column you would like to average
• Hit enter

EXAMPLE 1.2 — USING EXCEL TO FIND AN AVERAGE

• Let us again, average out the incomes from the apartment residents,
• But this time, we will use Excel (see the video below).
• Click here to download the file shown in the video below:

Sample vs population Notation

Populations

• A population is the entire group that you want to draw conclusions about
• The population mean is indicated by the symbol μ (mu)
• Ex: All students currently registered in the BCIT School of Business make up the population

Samples

• A sample is the specific group that you will collect data from that will not include all members of the population
• The sample mean is indicated by the symbol x̄ (x-bar)
• Ex: A randomly selected group of students from BCIT whose last name begins with the letter ”B”.

Key Takeaways (exercise)

Your Own Notes

• Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?
• These notes are for you only (they will not be stored anywhere)
• Make sure to download them at the end to use as a reference