Bell Ringer The graph below shows a distance

Bell Ringer • The graph below shows a distance versus time graph. What is the average speed between 2 p. m. and 4 p. m. ? A. B. C. D. 25 miles per hour 62. 5 miles per hour 75 miles per hour 137. 5 miles per hour

Topic 5 – Statistical Models Dot Plots, Histograms, and Box Plots Book Lesson 9. 2 and 9. 3 Pages 389 - 416 Homework 9. 2 – 5 -13, 14 -19, 23, 24 9. 3 – 1 -4, 6, 7, 13, 17, 19

• Measures of Center Review – Mean: the sum of all the values in the set divided by the number of values in the set. – Median: the middle value in the set, when the values are arranged in numerical order. – Mode: the most repeated value in the set. • Measures of Spread – Range: the difference between the larges and smallest value in the set. – Interquartile Range (IQR): the difference between the upper and lower quartiles (Q 3 – Q 1). – Standard deviation: the average of the distance between individual data values and the mean. The more spread out the data is, the higher the standard deviation.

Dot Plots • A dot plot is a data representation that uses a number line and Xs, dots, or other symbols to show frequency. Dot plots are sometimes called line plots. • Dot plots are the best option for displaying small sets of data or individual data values. • Dot plots are not appropriate for large sets of data.

• Twelve employees at a small company make the following annual salaries (in thousands of dollars): 25, 30, 35, 35, 40, 40, 45, 50, and 60. Create a Dot plot with the data.

The effects of an outlier in the data • An outlier is a value in a data set that is much greater or much less than most of the other values in the data set. • In the case of an outlier, the mean should NOT be used as a way to measure the center, instead, the median should be use. • Even when comparing two data sets where only one of them contains an outlier.

Comparing data distributions • A data distribution can be described as symmetric, skewed to the left, or skewed to the right, depending on the general shape of the distribution in a dot plot or other data display. • When comparing data sets, if both data sets seem to be symmetric, the mean or the mean could be use. • In the case that one of the data sets is skewed to the left or right, then ONLY the median can be used.

Histograms • A histogram is a bar graph that is used to display the frequency of data divided into equal intervals. • The bars must be of equal width and should touch but not overlap. The heights of the bars indicate the frequency of data values within each interval. • Histograms are useful when representing large sets of data. • Histograms are not useful to look at individual data values. They only show intervals.

Listed are the ages of the 100 U. S. senators at the start of the 112 th Congress on January 3, 2011. 39, 42, 44, 46, 47, 47, 48, 49, 49, 50, 51, 52, 53, 54, 55, 55, 55, 56, 57, 57, 58, 58, 58, 59, 59, 60, 60, 61, 62, 62, 63, 63, 64, 64, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 73, 74, 74, 75, 76, 76, 77, 78, 86, 86

B) Listed are the scores from a golf tournament. 68, 76, 71, 69, 73, 72, 74, 76, 70, 77, 74, 75, 76, 71, 74

Box Plots • A box plot can be used to show the values in a data set are distributed. • You need 5 values to make a box plot: the minimum (or least value), first quartile, median, third quartile, and maximum (or greatest value). • Each section of a box plot accounts for 25% of the data. Since there are 4 sections, that would make 100% of the data.

• Use the following data construct a Box Plot 13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 18, 22, 23

Practice • 9. 2 – Page 391: Problem 4 – Page 395: Problem 9 • 9. 3 – Page 403: Problem 4 – Page 406: Problems 8 and 9