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

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

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