2. Mean, Median, Mode & Range

3. Outlier An outlier is a data item that is much higher or much lower than items in a data set. 1, 2, 5, 27, 3, 4

4. Vocabulary Review Sum – the answer to an addition problem. Addend – the numbers you added together to get the sum. 6 + 9 = 15 BACK

5. Definition MeanMean – the average of a group of numbers. 2, 5, 2, 1, 5 Mean = 3 BACK

6. Mean is found by evening out the numbers 2, 5, 2, 1, 5 BACK

7. Mean is found by evening out the numbers 2, 5, 2, 1, 5 BACK

8. Mean is found by evening out the numbers 2, 5, 2, 1, 5 mean = 3 BACK

9. How to Find the Mean of a Group of Numbers Step 1 – Add all the numbers. 8, 10, 12, 18, 22, 26 8+10+12+18+22+26 = 96 BACK

10. How to Find the Mean of a Group of Numbers Step 2 – Divide the sum by the number of addends. 8, 10, 12, 18, 22, 26 8+10+12+18+22+26 = 96 How many addends are there? BACK

11. How to Find the Mean of a Group of Numbers Step 2 – Divide the sum by the number of addends. 6)6) 96 sum# of addends 1 6 36 6 63 BACK

12. How to Find the Mean of a Group of Numbers The mean or average of these numbers is 16. 8, 10, 12, 18, 22, 26 BACK You try this one

13. What is the mean of these numbers? 7, 10, 16 11 BACK

14. What is the mean of these numbers? 2, 9, 14, 27 13 BACK

15. What is the mean of these numbers? 26, 33, 41, 52 38 BACK

16. Definition MedianMedian – the middle number in a set of ordered numbers. 1, 3, 7, 10, 13 Median = 7 BACK

17. How to Find the Median in a Group of Numbers Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 27 18, 19, 21, 24, 27 BACK

18. How to Find the Median in a Group of Numbers Step 2 – Find the middle number. 21, 18, 24, 19, 27 18, 19, 21, 24, 27 BACK

19. How to Find the Median in a Group of Numbers Step 2 – Find the middle number. 18, 19, 21, 24, 27 This is your median number. BACK

20. How to Find the Median in a Group of Numbers Step 3 – If there are two middle numbers, find the mean of these two numbers. 18, 19, 21, 25, 27, 28 BACK

21. How to Find the Median in a Group of Numbers Step 3 – If there are two middle numbers, find the mean of these two numbers. 21+ 25 = 46 2)2) 23 median BACK

22. What is the median of these numbers? 16, 10, 7 10 7, 10, 16 BACK

23. What is the median of these numbers? 29, 8, 4, 11, 19 11 4, 8, 11, 19, 29 BACK

24. What is the median of these numbers? 31, 7, 2, 12, 14, 19 13 2, 7, 12, 14, 19, 31 12 + 14 = 26 2)2) BACK

25. Definition Ala mode mode – the most popular or that which is in fashion. Baseball caps are a la mode today. BACK

26. Definition ModeMode – the number that appears most often in a set of numbers. 1, 3, 7, 10, 13 Mode = 1 BACK

27. How to Find the Mode in a Group of Numbers Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 18 18, 19, 21, 24 BACK

28. How to Find the Mode in a Group of Numbers Step 2 – Find the number that is repeated the most. 21, 18, 24, 19, 18 18, 18, 19, 21, 24 BACK

29. Which number is the mode? 29, 8, 4, 8, 19 8 4, 8, 19, 29 BACK

30. Which number is the mode? 1, 2, 2, 9, 9, 4, 9, 10 9 1, 2, 4, 9, 10 BACK

31. Which number is the mode? 22, 21, 27, 31, 21, 32 21 21, 22, 27, 31, 32 BACK

32. Definition RangeRange – the difference between the greatest and the least value in a set of numbers. 1, 3, 7, 10, 13 Range = 12 BACK

33. How to Find the Range in a Group of Numbers Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 27 18, 19, 21, 24, 27 BACK

34. How to Find the Range in a Group of Numbers Step 2 – Find the lowest and highest numbers. 21, 18, 24, 19, 27 18, 19, 21, 24, 27 BACK

35. How to Find the Range in a Group of Numbers Step 3 – Find the difference between these 2 numbers. 18, 19, 21, 24, 27 27 – 18 = 9 The range is 9 BACK

36. 4, 8, 19, 29 What is the range? 29, 8, 4, 8, 19 29 – 4 = 25 BACK

37. What is the range? 22, 21, 27, 31, 21, 32 32 – 21 = 11 21, 22, 27, 31, 32 BACK

38. What is the range? 31, 8, 3, 11, 19 31 – 3 = 28 3, 8, 11, 19, 31 BACK

39. What is the range? 23, 7, 9, 41, 19 41 – 7 = 34 7, 9, 23, 19, 41 BACK

40. 17, 18, 19, 21, 24,26, 27 The lower quartile (LQ) is the median of the lower half of the data. The LQ is 18. The upper quartile (UQ) is the median of the upper half of the data. The UQ is 26. The interquartile range is UQ-LQ BACK

41. 13,15,18,19,22,25 Even amounts divide in 2 equal halves. L.Q. U.Q.

42. Key Skills Use data to construct a histogram. Jose bowled 11 games: 172, 152, 168, 157,143, 175,144, 164, 142, 172, 168. Histogram: TRY THIS

43. Find the median 76, 78, 82, 87, 88, 88, 89, 90, 91, 95 88 Find the median of this segment 82 76,78, 82 1 st quartile Find the median of this segment. 90 88, 89,90 3 rd quartile

44. 76, 78, 82, 87, 88, 88, 89, 90, 91, 95 Now for the box and whisker 65 70 75 80 85 90 95 Minimum End of 1 st quartile Median End of 3 rd quartile Maximum 100 105

45. Find the median 142, 143, 144, 152, 157, 164, 168, 168, 172, 172 175. 164 Find the median of this segment 144 142, 143, 144 1 st quartile Find the median of this segment. 172 168, 168, 172 3 rd quartile

46. 142, 143, 144, 152, 157, 164, 168, 168, 172, 172, 175. Now for the box and whisker 140 145 150 155 160 165 170 Minimum End of 1 st quartile Median End of 3 rd quartile Maximum 175 180

47. Rules and Properties Data Displays A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set. 1.Draw a number line and identify the median and the greatest and least values with vertical lines.

48. Rules and Properties Data Displays A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set. 2.Identify the lower quartile with a vertical line. The lower quartile is the median of all data in the lower half (below the median) of the data set.

49. Rules and Properties Data Displays A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set. 3.Identify the upper quartile with a vertical line. The upper quartile is the median of all data in the upper half (above the median) of the data set.

50. Rules and Properties Data Displays A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set. 4.Draw a rectangular box from the lower quartile to the upper quartile. 5.Draw lines from the ends of the box to the marks for the greatest and least values.

51. Key Skills Use data to construct stem-and-leaf plots, histograms, and box-and-whisker plots. Ten students had the following test scores on a math test: 88, 78, 82, 95, 90, 91, 87, 76, 88, 89. Box-and-whisker plot:

52. Mean: sum of all elements divided by the total number of elements. Median: middle number in a set when the elements are placed in numerical order. If there are an even number of elements, the median is the average of the two middle numbers. Rules and Properties

53. Mode: the element that occurs most often. There may be no mode, one mode, or several modes. Range: difference between the greatest and least values in a set. Rules and Properties

54. In one season, professional baseball teams in one division had 91, 78, 73, 73, and 66 wins. Find the mean, median, mode, and range for a set of data. median: Arrange the data in order: 66, 73, 73, 78, 91 mode: 73 (73 occurs twice in the set) range: 91 – 66 = 25 median mean: = 76.2 91 + 78 + 73 + 73 + 66 5 Key Skills

55. A quiz was given in Mr. Cucci’s Algebra Class with the following results. 7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10 Create a frequency table, find the mean, mode, median and range.

56. Construct a Frequency Table (tally sheet) Enter the data value into the 1 st column Data ValueTallyFrequency 0 1 2 3 4 5 6 7 8 9 10 7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10

57. Construct a Frequency Table (tally sheet) Enter a tally for each entry. Data ValueTallyFrequency 0 1 2 3 4 5 6 7 8 9 10 7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10

58. Construct a Frequency Table (tally sheet) Count the tallies and put the total for each value in the frequency column Data ValueTallyFrequency 0 1 2 3 4 5 6 7 8 9 10 1 2 1 4 4 2 3 In this way the mode and the median can easily be seen.

59. Introduction Using statistics is a helpful way to study different situations. Today I will demonstrate how to find the mean, median, and mode of a set of numbers.

60. Topics of Discussion The mean (or average) is found by taking the sum of the numbers and then dividing by how many numbers you added together. The number that occurs most frequently is the mode. When the number are arranged in numerical order, the middle one in the mean.

61. Topic One The mean (or average) is found by adding all the numbers and then dividing by how many numbers you added together. Example: 3,4,5,6,7 3+4+5+6+7= 25 divided by 5 = 5 The mean is 5

62. Topic Two The number that occurs most frequently is the mode. Example: 2,2,2,4,5,6,7,7,7,7,8 The number that occurs most frequently is 7 The mode is 7

63. Topic Three When numbers are arranged in numerical order, the middle one is the median. Example: 3,6,2,5,7 Arrange in order 2,3,5,6,7 The number in the middle is 5 The median is 5

64. Averaging Grades Lowest 55 60 75 80 83 93 Highest

65. Find The mean of the following set of grades First add all the grades together. The total equals 1061 Now divide 1061 by 13 (total grades The answer is 81.61 The mean is 81.61 Lowest 55 60 75 80 83 93 Highest

66. Find the median of the following numbers The median is the number in the middle of numbers which are in order from least to greatest. If we count from both sides the number in the middle is 83. The median is 83 Lowest 55 60 75 80 83 93 Highest

67. Find the mode of the following grades The mode is the number which occurs most often. The number which occurs most often is 93 The mode is 93 Lowest 55 60 75 80 83 93 Highest

68. Real Life If these were your math grades, what would you learn by analysising them? The mean was 81.61. In order to raise your grades, you would have to make higher than an 81.61 on the rest of your assignments. The mode was 93 which was your highest grade. You could look at these papers to see why you made this grade the most. The median is a 83. This means that most of your grades were higher than your average. Find your week area and try to improve.

69. Real Life –Knowing the mean, median, and mode will help you better understand the scores on your report card. By analyzing the data (grades) you can find your average, the grade you received most often, and the grade in the middle of your subject area. –Better understanding your grades may lead to better study habits.

71. Mean, Median, Mode & Range BACK