2.4 Stuff The range of a data set is the difference between the maximum and minimum data entries in the set. 2.4 Stuff The deviation of an entry x in a population data set is the difference between the entry and the mean of the data set. Deviation of x = x – 2.4 Stuff The population variance of a population data set of N entries is ( x ) 2 Population variance = N 2 The population standard deviation of a population data set of N entries is the square root of the population variance. 2 Population standard deviation = 2.4 Stuff The sample variance and sample standard deviation of a sample data set of n entries is 2 ( x x ) 2 Sample variance = s n 1 Sample standard deviation = s s2 2.4 Exercise #13 The sample data set is 4 15 9 12 16 8 11 19 14 2.4 Exercise #33/35 The mean value of land and buildings per acre from a sample of farms is $1,500, with a standard deviation of $200. The data set has a bell-shaped distribution. 33) Estimate the percent of farms whose land and building values per acre are between $1,300 and $1,700. 35) If the sample size is 75, estimate the number of farms whose land and building values per acre are between $1,300 and $1,700. 2.4 Stuff Chebychev’s Theorem. The portion of any data set lying within k standard deviations (k > 1) of the mean is at least 1 1 2 k if k = 2, then 75% of the data lies within 2 standard deviations if k = 3, then it’s 88.9%. 2.4 Stuff The sample standard deviation for a frequency distribution is ( x x ) 2 f s n 1 where n = f is the number of entries.