Statistics Unit Test Review Chapters 11 & 12

11-1/11-2 Mean(average): the sum of the data divided by the number of pieces of data Median: the value appearing at the center of a sorted list of values, or the mean of the two central values, if the list contains an even number of values Mode: the number or numbers that occur most often The mean, median, and mode are called measures of center

11-3 Measures of Variation Used to describe the distribution, or spread, of data Median First Quartile Third Quartile Interquartile Range Range

First Quartile Third Quartile Interquartile Range Range Median of the first half of data values Third Quartile Median of the second half of data values Interquartile Range Distance between the first and third quartiles If it is low, the middle data are grouped closely together Range Difference between the greatest and least data values

To find limits for outliers: Outlier: A data value that is either much greater or much less than the other values in a data set If the data value is more than 1.5 times the value of the IQR beyond the quartiles, it is an outlier To find limits for outliers: Find the IQR Multiply IQR by 1.5 Subtract that number from the first quartile and add it to the third quartile—any number beyond limits is an outlier

Find the limits for the outliers and name any outliers in the data. Find the range, median, first and third quartiles, and interquartile range for the data below. Find the limits for the outliers and name any outliers in the data. Test Grades 83 85 87 89 88 67 79 81

11-4 Mean Absolute Deviation: the average distance between each data value and the mean Can also be used to describe the spread of a set of data Steps to find MAD: Find the mean of the data set Find the distance each value is from the mean Find the average of these distances

Compare variations A data set with a smaller mean absolute deviation has data values that are closer to the mean than a data set with a greater mean absolute deviation Smaller mean absolute deviation = data are closer together

Pg. 840 #1 & 2

11-5 Appropriate Measures Most appropriate when… Mean: data have no extreme values Median: data have extreme values and/or there are no big gaps in the middle of the data Mode: data have many repeated numbers

Find the measure of center that best represents the data Find the measure of center that best represents the data. Justify your selection and then find the measure of center. number of parking spaces used: 46, 39, 40, 45, 44, 78, 51 golf scores over par: 3, 2, 0, 1, 3, 6, 4, 5

12-1 Line Plot/Dot Plot: visual display of a distribution of data values where each data value is shown as a dot or other mark, usually an x, above a number line

12-2 Histograms: type of bar graph used to display numerical data that have been organized into equal intervals Intervals allow you to see the frequency distribution of the data, or how many pieces of data are in each interval

Histogram Info: There is no space between bars Because all of the intervals are equal, all of the bars have the same width Intervals with a frequency of 0 have a bar height of 0

When constructing a histogram: Make frequency table first Have between 4-6 intervals Draw and label a horizontal and vertical axis Include a title Show the intervals from the frequency table on the horizontal axis Label the vertical axis to show the frequencies For each interval, draw a bar with the correct height

Pg. 877 #13-16

12-3 Box Plot/Box-and-whisker plot Uses a number line to show the distribution of a set of data by using the median, quartiles, and extreme values A box is drawn around the quartile values The whiskers extend from each quartile to the extreme data points that are not outliers The median is marked with a vertical line Separates the data into four parts each containing 25% of the data

Interpreting Box Plots If the length of a whisker or the box is short, the values of the data in that part are concentrated If the length of a whisker of the box is long, the values of the data in that part are spread out

Pg. 885 #12 After creating box plot, describe the data

12-4 Shape of Data Distributions The distribution of a set of data values shows the arrangement of data values Symmetric: data evenly distributed between the left side and right side Cluster: data grouped closely together Gap: no data values Peak: mode

Pg. 897 #10 Pg. 897 #12 graph only Directions: Use clusters, gaps, peaks, outliers, and symmetry to describe the shape of the distribution.