Common Core State Standards: Section 11.6 ANALYZING DATA Common Core State Standards: MACC.912.S-ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). MACC.912.N-Q.A.1: Use units as a way to understand problems and to guide the solution of multi-step problems choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

RATE YOUR UNDERSTANDING ANALYZING DATA MACC.912.S-ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). MACC.912.N-Q.A.1: Use units as a way to understand problems and to guide the solution of multi-step problems choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. RATING LEARNING SCALE 4 I am able to: calculate measures of central tendency to solve real world problems or more challenging problems that I have never previously attempted 3 calculate measures of central tendency draw and interpret box-and-whisker plots 2 calculate measures of central tendency with help draw and interpret box-and-whisker plots with help 1 understand how to interpret a box-and-whisker plot   TARGET

WARM UP Order the numbers from least to greatest. 1) 2)

KEY CONCEPTS AND VOCABULARY MEASURES OF CENTRAL TENDENCY MEAN MEDIAN MODE   First Quartile (Q1) – the median of the lower half of the data set Second Quartile (Q2) – the median of the data set (cuts the data in half) Third Quartile (Q3) – the median of the upper half of the data set

KEY CONCEPTS AND VOCABULARY MEASURES OF SPREAD RANGE INNER QUARTILE RANGE (IQR)

EXAMPLE 1: FINDING THE MEASURES OF CENTER FOR A DATA SET Find the mean, median, and mode of each data set. The numbers of hours Chris works each day are 8, 12, 7, 8, and 5 There are 25, 30, 24, 26, 21, and 30 students in a school’s seven Algebra 1 classes Mean: 8 Median: 8 Mode: 8 Mean: 26 Median: 25.5 Mode: 30

EXAMPLE 2: FIND MEASURES OF SPREAD FOR A DATA SET Find the range and interquartile range for each data set. 3, 8, 2, 6, and 5 135, 130, 150, 119, 150, and 152 Range: 6 Interquartile Range: 4.5 Range: 31 Interquartile Range: 20

KEY CONCEPTS AND VOCABULARY A box-and-whisker plot can be used to show how the values in a data set are distributed. You need 5 values to make a box plot: the minimum, first quartile, median, third quartile, and maximum. A percentile is a number from 0 to 100 that you can associate with a value x from a data set. It shows the percent of data that are less than or equal to x. OUTLIER An outlier is value in a data set that is much greater or much less than most of the other values in the data set. A data value x is an outlier if:

KEY CONCEPTS AND VOCABULARY BOX-AND-WHISKER PLOT

EXAMPLE 3: CALCULATING PERCENTILE All the scores on an Advanced Algebra final exam are shown below. 59 62 63 63 72 74 74 78 79 81 83 84 84 84 89 90 92 94 96 98 a) What percentile is the student who scored 89? 70th percentile   b) What score would be the 55th percentile? 84

EXAMPLE 4: CREATING BOX-AND-WHISKER PLOTS Use the data to make a box plot. Listed are the scores from a professional golf tournament.
 68 76 71 69 75 74 77 78 73 70

EXAMPLE 4: CREATING BOX-AND-WHISKER PLOTS Use the data to make a box plot. Listed is the number of cars that park in a parking garage at a mall for twelve days. 35 57 103 138 110 45 49 62 98 145 106

EXAMPLE 5: COMPARING BOX-AND-WHISKER PLOTS The bowling averages for two competitive bowling teams are given in the table. Use the data to make a box plot for each team on the same number line.      b) Compare the distributions of the bowling averages for each team. Bowling Team 1 202 145 172 182 167 150 132 128 Bowling Team 2 192 211 185 173 178 166 158 171 120 Example: Team 1 has a wider distribution than team 2. The range is larger for team 2, but the interquartile range is smaller for team 2. Team 1 has a lower median that team 2.

EXAMPLE 5: COMPARING BOX-AND-WHISKER PLOTS Which team is better? Explain. Does either team have outliers? Team 2 is better. Since the data spread for the interquartile is not as large for team 2, they are a more consistent team. The interquartile range contains high scores for team 2 and team 2 has a higher median than team 1. Yes, Team 2 has an outlier at 120.