Chapter1.2

# Chapter1.2 - 1.2 Describing Distributions with Numbers Key...

This preview shows pages 1–5. Sign up to view the full content.

1.2 Describing Distributions with Numbers Key Words in Section 1.2 Measuring center: Mean and Median Measuring spread: Quartile , Standard Deviation and Variance Although graphs give an overall sense of the data, numerical summaries of features of the data make more precise the notions of center and spread.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Measuring center Two important measures of center are the mean and the median . The mean X One measure of center is the mean or average. The mean is defined as follows, suppose we have a list of numbers denoted, 1 x 2 x , …, n x . That is, there are n numbers in our list. The mean or average x-bar ( x ) of our data is defined by adding up all the numbers and dividing by the total of numbers. In symbols this is, = = + + + = n i i n x n n x x x x 1 2 1 1 where i x means the i th data value and Σ means “add up all these numbers.” . Please look at Example 1.14 in page 32 in our textbook.
The median M The median M is the midpoint of a distribution, the number such that half the observations are smaller and the other half are larger. How to find the median. 1.Order observations from smallest to largest. 2.If n is odd, the median is the value of the center observaton. Location is at ( n +1) / 2 in the list. 3.If n is even, the median is defined to be the average of the two center observations in the ordered list. Please look at Example 1.15 in page 33 in our textbook.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Measuring Spread Measures Based on the Quartiles Before we define quartiles, let’s think about percentiles in general. Examples of percentiles like the 95th percentile for height mean that if I am at the 95th percentile for height (I am roughly), it means that 95 percent of the population has a height less than mine. So we can now define some special percentiles:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

Chapter1.2 - 1.2 Describing Distributions with Numbers Key...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online