1. Algebra 2 Section 12-3 Analyzing Data

2. Algebra 2 Lesson 12-3 Analyzing Data Find the mean, median, and mode for these values: 78, 87, 84, 75, 80, 98, 78, 95, 72. The mean is 83, the median is 80, and the mode is 78. 72 75 78 78 80 84 87 95 98Find the median and the mode by ordering the values numerically. Mode Median (78 + 87 + 84 + 75 + 80 + 98 + 78 + 95 + 72) 9 747 9 = = 83 x = Use the symbol to designate the mean. x Additional Examples

3. Algebra 2 Lesson 12-3 Analyzing Data Using the data in the table, find the mean, median, and mode for the water temperatures in Dauphin Island, AL. Gulf of Mexico Eastern Coast Water Temperatures (°F) LocationJFMAMJJASOND Dauphin Island, Alabama 515360707582848480726256 Step 1:Use the STAT feature to enter data as L1 in your graphing calculator. Step 2:Use the LIST feature to access the MATH menu. Find the mean. Additional Examples

4. Algebra 2 Lesson 12-3 Analyzing Data (continued) Step 3:Return to the same menu to find the median. The mean is about 69.1°F, the median is 71°F, and the mode is 84°F. Additional Examples

5. Algebra 2 Box and Whisker Plots – when data are arranged in increasing order, the median divides the data into tow equal parts. You can use the median of each of these parts to divide the data further into four equal parts. The value separating these parts are called quartiles (lower/higher)

6. Algebra 2 Make a box-and-whisker plot for these values: 91, 95, 88, 85, 90, 97, 94, 100, 81. Lesson 12-3 Analyzing Data The minimum value is 81 and the maximum value is 100. Step 1: Find the quartile values, the minimum value, and the maximum value. 81 85 88 90 91 94 95 97 100 Q 2 = median = 91 The median is a value of the data set, it is removed for the calculation of Q 1 and Q 3. 81 85 88 90 94 95 97 100 Q 1 = = 86.5Q 3 = = 96 (85 + 88) 2 (95 + 97) 2 Additional Examples

7. Algebra 2 (continued) Lesson 12-3 Analyzing Data Step 2: Draw a number line for the base of your box-and-whisker plot. Above the number line, plot the three quartiles, the minimum value, and the maximum value. Step 3:Finish your box-and-whisker plot by drawing a box through Q 1 and Q 3, a vertical line through the median, and line segments from the box outward to the minimum and maximum values. Additional Examples

8. Algebra 2 Lesson 12-3 Analyzing Data Use a graphing calculator to find the quartiles of the water temperature data for Dauphin, AL in Additional Example 2. Use the TRACE feature to find the quartile values. They are Q 1 = 58, Q 2 = 71, and Q 3 = 81. Use the STAT PLOT feature to select a box-and-whisker plot. Enter the window values.Graph the box-and-whisker plot. Additional Examples

9. Algebra 2 Find the 30th and 60th percentiles for the values below. Lesson 12-3 Analyzing Data 54 98 45 87 98 64 21 61 71 82 93 65 62 98 87 24 65 97 31 47 Step 1: Order the values. 21 24 31 45 47 54 61 62 64 65 65 71 82 87 87 93 97 98 98 98 Step 2: Find the number of values that fall below the 30th percentile and the number that fall below the 60th percentile. Of the 20, 30% should fall below the 30th percentile and 60% should fall below the 60th percentile. 20  30% = 20  0.30 = 6 Since 61 is greater than 6 values, 61 is at the 30th percentile. The value at the 30th percentile is 61 and the value at the 60th percentile is 82. 20  60% = 20  0.60 = 12 Since 82 is greater than 12 values, 82 is at the 60th percentile. Additional Examples

10. Algebra 2 Outlier – is an item of data with a substantially different value from the rest of the items in the data set. Sometimes an outlier is an important part of the data. At other times it can represent a false reading. When you are sure an outlier is erroneous, you may remove it from the data set.

11. Algebra 2 15 26 28 30 32 34 34 Order the data. Lesson 12-3 Analyzing Data Identify an outlier for this set of values: 15 34 28 32 30 26 34. 15 is substantially different, so 15 is an outlier. Find the differences between adjacent values. 1122220 Additional Examples

12. Algebra 2 Checking For Understanding – Link is Below on website