Displaying Distributions Shape Histograms A histogram uses adjacent bars to show the distribution of values in a quantitative variable Each bar represents the frequency relative frequency of values falling in an interval of values o The standard rule for a value that falls exactly on a bin boundary is to put it into the next higher bin Stem and Leaf Displays quantitative data values in a way that sketches the distribution of the data It s best described in detail by example a stem and leaf display shows Shape The visual appearance of the distribution To describe the shape look for simple vs multiple modes and symmetry vs skewness distribution of a variable The apparent location of modes can change as the scale of a histogram is changed A peak or local high point in the shape of the Modes Distributions with two modes Having one mode Generally mound shaped o Unimodal o Bimodal o Multimodal o A distribution whose histogram doesn t appear o have any mode and in which all the bars are approximately the same height is called uniform Distributions with more than two modes Symmetry o Symmetric a distribution is symmetric if the two halves on either side of the center look approximately like mirror images of each other The thinner ends of a distribution are called he tails If one tail stretches out farther than the other the distribution is said to be skewed to the side of the longer tail Outliers Extreme values that don t appear to belong with the rest of the data They may be unusual values that deserve further investigation or just mistakes there s no obvious way to tell Sigma means sum y total n y n this gives you the o The mean is a natural summary for unimodal symmetric distributions it can be misleading for skewed data or for distributions with gaps or outliers the middle value with half of the data above it and Median half below it Center mean Spread of the Distribution Range defined as the difference between the extremes Range max min Interquartile Range IQR and third quartiles IQR Q3 Q1 The difference between the first The average of the squared deviations is called the variance Standard Deviation A measure of spread found as Shape Center and Spread If the shape is skewed point that out and report the median and IQR May want to include the mean and standard deviation as well explaining why the mean and median differ The fact that the mean and median do not agree is a sign that the distribution may be skewed Histogram will help make your point If the shape I unimodal and symmetric report the mean and standard deviation and possibly the median and IQR as well For unimodal symmetric data the IQR is usually a bit larger than the standard deviation Always pair the median with the IQR and the mean with he standard deviation Five Number Summary and Boxplots Five Number Summary Boxplot A five number summary for a variable consists of the minimum and maximum the quartiles Q1 and Q3 the median central box with whiskers that extend to the non outlying values Boxplots are particularly effective for comparing groups SEE NOTES ON HOW TO MAKE A BOXPLOT A boxplot displays the 5 number summary as a
View Full Document
Unlocking...