Chapter 3 (Sp11)

Chapter 3 (Sp11) - Section 3.1 Measures of Central Tendency...

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Section 3.1 – Measures of Central Tendency A measure of center is a value at the center (or middle) of a data set. Notation: x = variable representing data values n = total number of values in the sample = sum or “add up” N = total number of values in the population (difficult to know) Arithmetic Mean – Add the data values and divide by the total number of values. x = sample mean = n x Σ = sum of the data values divided by n (statistic) μ = population mean = N x Σ (parameter) Median – Data point that lies in the middle of the data set when arranged from smallest to largest. If you have an ODD number of values, the median will be the middle value. + 2 1 n If you have an EVEN number of values, take the average of the middle two values. + 1 2 2 n and n 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 Mode – The value that occurs most often. The data set can be bimodal, multimodal, or have no mode. (you can find the mode of qualitative data, too!) When data are skewed left or right, that means there are extreme values in the tail which are pulling the mean in the direction of the tail. (see Table 4 on pg. 134) Distribution Shape Mean vs. Median Skewed Left Mean < Median Symmetric Mean = Median Skewed Right Mean > Median Example : Find the mean, median, and mode for the following data set. 1
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(flight times in minutes of six flights from Las Vegas to Newark on Continental Airlines) 282 270 260 266 257 260 Finding Mean and Median on the calculator : 1. Enter the data into a list (L 1 ) 2. Select STAT 3. Arrow over to the menu labeled “CALC” 4. Highlight “1-VAR STATS” and push enter. 5. Type the name of the list (L 1 or L 2 , etc.) 6. Push enter and scroll down. Note : The default list for 1-VarStats is L 1 A numerical summary of data is resistant if extreme values (very large or small) do not affect its value substantially. Which of the following is considered resistant: Mean or Median? Section 3.2 – Measures of Dispersion 2
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Range = highest value – lowest value Variance is based on how the data points deviate from the mean. Variance of a sample
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This note was uploaded on 01/06/2012 for the course MATH 1342 taught by Professor Lisajuliano during the Spring '12 term at Collins.

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Chapter 3 (Sp11) - Section 3.1 Measures of Central Tendency...

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