STAT 210 1st Edition Exam 2 Study Guide Lectures 7-12Lecture 7 (Sep 9th) What does descriptive statistics describe? - Center of the distribution, spread of the distribution, shape of the distribution, any unusual features in the distribution- Qualitative data is in bar graphs and pie charts, quantitative data is divided into class interest, each measurement should fall in one and exactly one interval- Stem and Leaf Plot can be used to sort large list of data; can graphically display distribution, determine center of distribution, shape of distribution, determine any unusual features (any range of values not represented, concentration of data,any outliers)Advantages of a stem and leaf plot?- Display the distribution of the data, can be used to determine the center, spread, shape, and any unusual features of the distribution, retain the actual data, easy to construct, and make sorting of the data easierDisadvantages?- Not very effective for large data sets (would take a long time to construct), choiceof the stems depends on the data type and data range. Also different choices for the stems can cause different looking distributions.Lecture 8 (Sep 11th)What do histograms do?- Display quantitative data, don’t retain original data, only 1 class interval- Their purpose is to determine the number of class intervals to use. One rule is tocalculate the square root of the sample size, and round up. They determine the range of the data by subtracting the smallest observation from the largest observation. They divide the range by the number of class intervals and round to a convenient number. Lecture 9 (Sep 13th)Define the shapes of distributions- Symmetric: left and right are mirror images; Normal: looks like a bell-shaped curve (most common); Skewed left: bell shape with a long tail to the left; Skewed right: bell shape with a long tail to the right; Bimodal: 2 significant peaks; Trimodal: 3 significant peaks Unusual features of a graph?- High concentrations of data, gaps, extreme values (outliers)Lecture 10 (Sep 16th)Population symbols?-  = mean;  = standard deviation;  = proportionSample symbols?- X bar = sample mean; s = standard deviation; p hat = proportionHow to calculate median?-  = pop. Median- M = sample median- Order data from smallest to largest- Calculate median location (n+1)/2- Calculate median- If n is odd then (n+1)/2 and you’ll get a whole number- If n is even then (n+1)/2 will be a fractionWhat about distributions?- Mean is point where a histogram balances- For symmetric distributions mean and median will be nearly the sameLecture 11 (Sep 18th)What is range, standard deviation and interquartile range?- Range is maximum value – minimum value- Standard deviation is measure of variability about the mean- Interquartile range is the computer measure of spread around the medianDifference between upper and lower quartile range- Lower quartile (observations with 25% of the data less than it and 75% of the data greater than it); denoted as Q1- Upper quartile (observations with 75% of the data is less than it and 25% of the data is greater than it); denoted as Q3Lecture 12 (Sep 20th) Difference between mean and median- Mean is influenced by outliers; Population mean denoted by ; Sample mean denoted by x bar- Median is resistant to outliers; Population median denoted by ; Sample median denoted by MWhat are boxplots?- A graphical display which uses several of the numerical measures to give information on the symmetry of shape of the distribution, the central location and variability (spread) in a distribution and on the concentration of scores in tails of distribution (outliers)Types of boxplots- A symmetric boxplot with long whisker or several outliers at each end indicate that the data may come from a distribution with long tails; occasionally called long-tailed distributions- A skewed boxplot or a boxplot with several outliers indicates that the data is either from a skewed distribution or a distribution with long tails. A boxplot is skewed if the median is not in the center of the box or if one of the adjacent values is closer to the box than the other.- Side-by-side boxplots can be constructed and used to compare the distributions of several distributions. To create side-by-side boxplots, label one axis and draw several boxes next to