Data Set 1: 7, 7, 8, 9, 10, 10, 10, 20, 25 Data Set 2: 7, 7, 8, 9, 10, 10, 10, 20, 100
1. Find the mean, median and mode of each data set.
2. Which one, the mean, median, or mode, is the most accurate number to use to represent each data set?

Reminder: When finding mode -

  • If _____ entry is repeated the data set has ______.
  • If ______entries occur with the same greatest frequency, each entry is a mode (______).

Sigma notation:
Population mean:
Sample mean:

Comparing the Mean, Median, and Mode

All three measures describe a typical entry of a data set.
______: useful for predicting future results when there are ______ in the data set
______: more useful than the mean when there are ______ in the data set as it is not affected bythe extreme values
______: useful when the most common item, characteristic or value of a data set is required. It is also the most useful when describing ______ (______).

Example: Find the mean, median, and mode of the sample ages of a class shown. Which measure of central tendency best describes a typical entry of this data set? Are there any outliers?

Sometimes a graphical comparison can help you decide which measure of central tendency best represents a data set.

Weighted Mean

Example: You are taking a class in which your grade is determined from five sources: 50% from your test mean, 15% from your midterm, 20% from your final exam, 10% from your computer lab work, and 5% from your homework. Your scores are 86 (test mean), 96 (midterm), 82 (final exam), 98 (computer lab), and 100 (homework). What is the weighted mean of your scores?

Practice: The mean scores for a statistics course (by major) are given. What is the mean score for the class?

8 engineering majors: 83

5 math majors: 87

11 business majors: 79

Mean of a Frequency Distribution

Example: Use the frequency distribution to approximate the mean number of minutes that a sample of Internet subscribers spent online during their most recent session.

Practice: Use the frequency distribution to approximate the mean height (in inches) of 16 female students in a physical education class.

The Shapes of Distributions

Symmetric Distribution
A vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately mirror images.
/ Uniform Distribution (rectangular)
All entries or classes in the distribution have equal or approximately equal frequencies.

Skewed Left Distribution (negatively skewed)
  • The “tail” of the graph elongates more to the left.
  • The mean is to the left of the median.
/ Skewed Right Distribution (positively skewed)
  • The “tail” of the graph elongates more to the right.
  • The mean is to the right of the median.