Transcript 1.2 PII
Section 1.2 Part II Special Problem Guidelines posted online – start today! Standard Deviation: A measure of spread Standard deviation looks at how far observations are from their mean. It’s the natural measure of spread for the Normal distribution We like s instead of s-squared (variance) since the units of measurement are easier to work with (original scale) S is the average of the squares of the deviations of the observations from their mean. Etc… S, like the mean, is strongly influenced by extreme observations. A few outliers can make s very large. Skewed distributions with a few observations in the single long tail = large s. (S is therefore not very helpful in this case) As the observations become more spread about the mean, s gets larger. Mean vs. Median Standard Deviation vs. 5-Number Summary The mean and standard deviation are more common than the median and the five number summary as a measure of center and spread. No single # describes the spread well. Remember: A graph gives the best overall picture of a distribution. ALWAYS PLOT YOUR DATA! The choice of mean/median depends upon the shape of the distribution. When dealing with a skewed distribution, use the median and the 5# summary. When dealing with reasonably symmetric distributions, use the mean and standard deviation. The variance and standard deviation are… LARGE if observations are widely spread about the mean SMALL if observations are close to the mean Degrees of Freedom (n-1) Definition: the number of independent pieces of information that are included in your measurement. Calculated from the size of the sample. They are a measure of the amount of information from the sample data that has been used up. Every time a statistic is calculated from a sample, one degree of freedom is used up. If the mean of 4 numbers is 250, we have degrees of freedom (4-1) = 3. Why? ____ ____ ____ ____ mean = 250 If we freely choose numbers for the first 3 blanks, the 4th number HAS to be a certain number in order to obtain the mean of 250. A person’s metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting, and exercise. Here are the metabolic rates of 7 men who took part in a study of dieting: 1792 1666 1362 1614 1460 1867 1439 Find the mean Column 1: Observations (x) Column 2: Deviations Column 3: Squared deviations (TI-83: STAT/Calc/1-var-Stats L1 after entering list into L1) You do! (Long Way Round) Let X = 3,7,15, 23 What is the variance and standard deviation? You do! (using 1 Var Stats) During the years 1929-1939 of the Great Depression, the weekly average hours worked in manufacturing jobs were 45, 43, 41, 39, 39, 35, 37, 40, 39, 36, and 37. What is the variance and standard deviation? Miami Heat Salaries 1) Suppose that each member receives a $100,000 bonus. How will this effect the center, shape, and spread? 2) Suppose that each player is offered 10% increase in base salary. What happened to the centers and spread? Player Salary Shaq 27.7 Eddie Jones 13.46 Wade 2.83 Jones 2.5 Doleac 2.4 Butler 1.2 Wright 1.15 Woods 1.13 Laettner 1.10 Smith 1.10 Anderson .87 Dooling .75 Wang .75 Haslem .62 Mourning .33