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ams 102 chapter 5 - Chapter 5 Summarizing Data Numerically...

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Page 1 of 5 Chapter 5: Summarizing Data Numerically Measures of center - mean - median - mode (mainly for qualitative data) The average or mean is a measure of center (middle of a set of data) If our data is a sample, then the mean is a statistic x (pronounced “x-bar”) If our data is a population, then the mean is a parameter (pronounced “mu”) mean = sum of observation values divided by the # of total observations sample mean: 1 1 2 ... n i i n x x x x x n n = + + + = = ° Ex. 1 What’s average amount of time to finish a 5K race? Sample of 5 participants (times rounded to nearest minute) 45 53 45 50 48 Ex. 2 Let’s Do It! 5.2 We have 7 students. The mean score for 3 of these students is 54 and the mean score for the other 4 students is 76. What is the mean score for all seven students? Ex. 3 What happens if the last number in Ex. 1 was an 80 instead of 48? Find the new mean 45 53 45 50 80 The mean is influenced by extreme values – we won’t get an accurate value for where the middle of the data is. For skewed distributions (extreme values present) the median is a better measure of center. median – value that cuts the ordered data into ½. The median is resistant to extreme values Finding the median 1. Arrange the observations in increasing order 2. If the # of observations is odd, the median is the value at the 1 2 n + th location
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Page 2 of 5 If the # of observations is even, the median is the average of the values at the 2 n th and 1 2 n ± ² + ³ ´ µ th location Ex. 4 Find median of following values: 45 53 45 50 48 Ex. 5 Find median of following values: 45 53 45 50 48 55
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