States The stem-and-leaf display shows populations of the 50 states and Washington, DC, in millions of people, according to the 2000 census. 3 2 2 1 1 0 0 State Populations (1 2 means 12 million) 4 1 6 0 5 1 9 1 5 1 2 5 1 2 5 1 6 1 6 1 6 1 6 1 6 1 7 1 8 1 8 1 8 122222333333344444 a) What measures of center and spread are most appropriate? b) Without doing any calculations, which must be larger: the median or the mean? Explain how you know. c) From the stem-and-leaf display, find the median and the interquartile range. d) Write a few sentences describing this distribution

Variation of sample mean: With a population standard deviation of σ , the variation of the sample means is σX´ , which the standard deviation of the sample mean: σX= σ √n But if we don’t know the population standard deviation, σ , we use the sample standard deviation, S, to approximate the population standard deviation, and the variation of sample means becomes the standard error of the sample mean: S SEX= √ n In general, as long as outcomes of each trial are independent and from a fixed population (random & no replacement or large population relative to sample), then variation of sample ratio is inversely proportional to square root of sample size: