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Statistics Assumed you have had this in previous math classes… What are measures of central tendency? How do you tell measures of central tendency apart? What is standard deviation? How is it calculated? An intro to Statistics • Statistics – numerical values used to summarize & compare sets of data (such as ERA in baseball). • Measures of Central Tendency – mean, median, & mode are the 3 we will be using. Tells you what the “center” of the data is. Mean – ( x ) average of n numbers (add all #s & divide by n) Median – the middle # when the #s are written in order from least to greatest or greatest to least. If there are 2 middle numbers, the median will be the average of those 2. Mode – the number(s) that occur most frequently. It is possible to have more than 1 mode or even no mode. Ex: Find the mean, median, & mode of the following set of numbers: 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24. • Mean - 445 34.2 13 Median – Put the numbers in order first! 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48 Mode – most frequent! 40 is the mode. Measures of Dispersion – tell how spread out the data are. * Range – Difference between the largest and smallest values. (for example: the range of the last example would be 48-17=31) * Standard Deviation - (σ – “sigma”) ( x1 x) 2 ( x2 x) 2 ... ( xn x) 2 x is the mean n x1, x2, x3, …, xn are the entries in the data set. n is the number of entries in the set x is the mean Standard Deviation symbol - (σ – “sigma”) Standard deviation describes the typical difference (deviation) between the mean and a data value. “A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values. Standard deviation is commonly used to measure confidence in statistical conclusions.” http://en.wikipedia.org/wiki/Standard_deviation This is why you see standard deviation on test scores. Ex: Find the standard deviation of the data from the first example. (36 34.2) 2 (39 34.2) 2 (40 34.2) 2 ... (24 34.2) 2 13 856.32 13 65.87 8.12 What are measures of central tendency? Mean, medium and mode How do you tell measures of central tendency apart? Mean=average, median=middle, mode=appears most often What is standard deviation? How is it calculated? Standard deviation=typical difference between the mean and a data value. Assignment Worksheet 7.7