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**Ch 11 – Probability & Statistics**

11.5 – Measures of Central Tendency and Variation – Day 2

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**A measure of variation is a value that describes the spread of a data set.**

Range Interquartile range Variance Standard deviation The variance, denoted by σ2, is the average of the squared differences from the mean. Standard deviation, denoted by σ, is the square root of the variance and is one of the most common and useful measures of variation.

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**To find the variance and standard deviation**

Find the difference between the mean and each data value, and square it Find the variance,σ2 , by adding the squares of all of the differences from the mean and dividing by the number of data values. Find the standard deviation, σ, by taking the square root of the variance.

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Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops. {6, 8, 7, 5, 10, 6, 9, 8, 4} Find the mean. Find the difference between the mean and each data value, and square it. Find the variance. Find the standard deviation. x 6 8 7 5 10 9 4 x – x (x – x)2 Average of last row σ2 ≈3.33… Square root of variance σ ≈ 1.8

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**An outlier is an extreme value that is much less than or much greater than the other data values.**

If an outlier is the result of measurement error or represents data from the wrong population, it is usually removed. One method to find outliers is to look for data values that are more 3 standard deviations from the mean.

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**Find the mean and the standard deviation for the heights of 15 cans**

Find the mean and the standard deviation for the heights of 15 cans. Identify any outliers, and describe how they affect the mean and the standard deviation. (Use a calculator!!!) Can Heights (mm) 92.8 92.9 92.7 92.1

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**To use a calculator for this**

Enter the data into a list. Push STAT CALC 1-VAR STATS What does it tell you? How would you find if there is an outlier? Then, if any part of the data lies outside that, it is an outlier.

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**If you take out the outlier (delete it), what is the new mean and standard deviation?**

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Standard Deviation A Measure of Variation in a set of Data.

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