3.2 Finding the Center of a Data Set. Mean, Median, Mode Theory

3 Ways to Describe the Center of Your Data Set

(1) Mean (Arithmetic Average)

(2) Median (Middle)

(3) Mode (Most)

What is the mean?

(1) arithmetic average

(2) what you know as taking the average

How to Find the Mean

(1) Arithmetic Average

(2) add all the values, divide by the number of values added

Sample Mean Formula

Population Mean Formula

What is the median?

(1) the middle

How to Find the Median

Step 1: Order values

Step 2: Find middle value

• Odd Number of Data Values

  • choose the middle value

• Even Number of Data Values

  • choose the middle 2 values, take the mean

What is the mode?

(1) what happens most in a data set

4 Outcomes of the Mode

(1) Single mode

(2) Bimodal

(3) Multimodal

(4) No mode

Rounding Rule of Thumb

(1) round the number to one decimal place more than what they gave you

Rounding Rule of Multiple-Step Formulas

(1) cannot round until the very last step when using multiple formulas

Steps to Finding the Mean of Frequency Distribution

Step 1: Class Midpoint

• Create a new column, x, which will represent the class midpoint

Step 2: Frequency * Midpoint

• Create a new column, f * x, which will represent the “mid-point” frequencies

Step 3: Take the average

• (1) Add up mid-point frequencies

• (2) Add up frequencies

• (3) Take the average by dividing; mid-point frequencies divided by the frequencies

Formula for Mean of Frequency Distribution

Table for Mean of Frequency Distribution

What is weighted distribution?

(1) essentially your GWA

Steps to Finding the Mean of a Weighted Distribution

Step 1: Convert scores to points

• Create new column, x, which will represent the points

• Essentially convert to percentage or something out of 100

Step 2: Weight * Points

• multiply the weighted grade by the points you got, just multiply across

• Create a new column, x * w, which will represent weighted-points

Step 3: Take the mean

• (1) Add up weighted points

• (2) Add up weights (which would obviously eventually add up to 100%)

• (3) Take the average

Formula for Mean of Weighted Distribution

Table for Mean of Weighted Distribution

Shape for Skewed Right

Shape for Skewed Left

Normal Shape

The difference between mean and median.

(1) the median is not affected by outliers, while the mean is affected by outliers