Measures: Mean, Median, Mode, and Range- Step-by-Step Lesson. mean = median = mode = range =

Transcription

1 Name Measures: Mean, Median, Mode, and Range- Step-by-Step Lesson Lesson 1 Statistics Problem: 1. Find the mean, median, mode, and range of the data set: 18, 17, 21, 21, 24, 16, 29, 18, 21,17 mean = median = mode = range = Explanation: The "mean" is the "average", where we add up all the numbers and then divide by the number of integers we used. Mean = The "median" is the "middle" value in the list of numbers. The best way to determine this is to write all the numbers in numerical order. We can use one of the following formulas to determine the position of the median in that set. When the numbers of element in set are odd then use this formula: Median = Mode is the data item that occurs most often. The "range" is just the difference between the largest and smallest values. mean = = 20.2

2 Name The number of element in set is 10 which is even number. Median = = = 5.5 (Position 5.5 means that we take the average between the 5 th and 6 th position.) 16, 17, 17, 18, 18, 21, 21, 21, 24, 29 If we average 18 and 21, we get: Median is: , 17, 17, 18, 18, 21, 21, 21, 24, 29 Mode = The item that occurs most often. Mode is: 21 Range = = 13 Answer is: 13

3 Name Measures: Mean, Median, Mode, and Range - Guided Lesson Complete the following problems: 1. Tommy has the following data: 17, 17, 15, 16, n If the mean is 14, which number should n be? (a) 15 (b) 5 2. Some farmers compared how many tractors were on their farm. Farmer Number of Trackers Farmer Jones Farmer Davis Farmer Thomas Farmer Robin Farmer Lee What was the median number of tractors the farmers had? 3. Find the mean, median, mode, and range of the data set: 55, 44, 42, 70, 56, 64, 44, 63, 39 mean = median = mode = range =

4 Name Measures: Mean, Median, Mode, and Range - Guided Lesson Explanation Explanation#1 The mean is the average of the numbers. We have to find out the mean by adding the numbers together and then dividing by the number of numbers in the group. There are 5 numbers in the group. If the average was 14, that would mean that the sum of all numbers would be: 5 x 14 = 70 To find the number, we solve: n = n = 70 (subtract 65 from both sides) n = 5 When n = 5, the mean is 14. Explanation#2 The median is the middle number of the data set. There are 5 pieces of data. Let s list the data in numeric order: 1, 2, 3, 3, 4 We can use this formula to determine the position of data: Median = Median = = = 3rd number of tractors 1, 2, 3, 3, 4 The median is 3 tractors.

5 Name Explanation#3 The "mean" is the "average" we are used to, where we add up all the numbers and then divide by the number of numbers. Mean = The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so we may have to rewrite our list first. Median = Mode is the data item that occurs most often. The "range" is just the difference between the largest and smallest values. mean = = 53 Median = = = 5 (position 5 in numeric order) 39, 42, 44, 44, 55, 56, 63, 64, 70 Median is 55. Mode = 39, 42, 44, 44, 55, 56, 63, 64, 70 Item that occurs most often. Mode is: 44 Range = = 31 Answer is: 31

6 Name Measures: Mean, Median, Mode, and Range - Independent Practice Worksheet Complete all the problems. 1. Find the mean, median, mode, and range of the data set: 8, 6, 7, 5, 6, 2, 5, 9, 9, 4, 5 mean = median = mode = range = 2. Lewis has the following data: 2, 5, m, 2, 4, 3 If the mean is 3, which number could m be? (a) 2 (b) 3 3. Some boys compared how many footballs they had: Farmer Footballs Long Sanders James Peterson Cole Jordon Owens What was the median number of footballs?

7 Name 4. Find the mean, median, mode, and range of the data set: 4, 17, 17, 4, 27, 29, 20, 24, 34, 4 mean = median = mode = range = 5. Allen has the following data: 4, 5, 8, p, 7, 6 If the mean is 6, which number could p be? (a) 6 (b) 7 6. Find the mean, median, mode, and range of the data set: 22, 24, 26, 20, 29, 28, 26 mean = median = mode = range = 7. Some teacher compared how many students were in their class. Teacher Number of Students Mr. Hall Mr. Garcia Mr. Taylor Mr. Moore Mr. Wilson What was the mode number of students the teacher had?

8 Name 8. Find the mean, median, mode, and range of the data set: 11, 13, 11, 12, 10, 12, 11, 8 mean = median = mode = range = 9. Adams has the following data: 2, t, 6, 5, 3 If the mean is 4, which number could t be? (a) 4 (b) Find the mean, median, mode, and range of the data set: 8, 7, 9, 14, 12, 7, 6 mean = median = mode = range =

9 Name Measures: Mean, Median, Mode, and Range - Matching Worksheet Write the letter of the answer that matches the problem. 1. Find the mean, median, mode, and range of the data set: 12,15,17,16,10 a. 5 mean = median = mode = range = 2. Nelson has the following data: 3, 8, 5, 4, f IF the mean is 5, which number could f be? b. Mean = 14, Median= 15, Mode = None, Range = 7 (a) 20 (b) 5 3. Some children compared how many candies they had: Children Number of Candy Carter c. Mean = 16, Median = 16, Mode = None, Range = 8 King Parker Evans Scott What was the median of the data set? 4. Find the mean, median, mode, and range of the data set: 14, 18, 12, 20 mean = mode = median = range = d. 2

10 Topic : Mean, Median, Mode -Worksheet 1 Calculate mean, Median and Mode for each dataset Mean Median Mode

11 Topic : Mean, Median, Mode -Worksheet 2 Calculate mean, Median and Mode for each dataset Mean Median Mode

12 Topic : Mean, Median, Mode -Worksheet 3 Calculate mean, Median and Mode for each dataset Mean Median Mode

13 Topic : Mean, Median, Mode -Worksheet 4 Calculate mean, Median and Mode for each dataset Mean Median Mode

14 Topic : Mean, Median, Mode -Worksheet 5 Calculate mean, Median and Mode for each dataset Mean Median Mode

15 Topic : Mean, Median, Mode, and Range- Worksheet 1 Calculate Mean, Median, Mode and Range for each data set

16 Topic : Mean, Median, Mode, and Range- Worksheet 2 Calculate Mean, Median, Mode and Range for each data set

17 Topic : Mean, Median, Mode, and Range- Worksheet 3 Calculate Mean, Median, Mode and Range for each data set

18 Topic : Mean, Median, Mode, and Range- Worksheet 4 Calculate Mean, Median, Mode and Range for each data set

19 Topic: Mean, Median, Mode, and Range- Worksheet 5 Calculate Mean, Median, Mode and Range for each data set

20 Topic : Central Tendency - Mean, Mode, Median - Worksheet 1 Andy consumes 1.1, 3, 2.5, 2.1, 3.2, 2.5, 1.4, and 2.5 grams of bread respectively in a week. Find the following measures of central tendency based on Andy s data: 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Prepare a frequency distribution with a class interval of 0.6 for the above data set. Bread amount Frequency Find the modal interval. 6. What would be the mean amount of bread Andy consumed, if he consumes 0.3 g more bread every day? 7. What would be the mode if he consumes 0.2 g more bread every day? 8. What value is the value of n if 8, 4 and n have the same mean as that of 4 and 10? 9. On his first 5 math tests Mark received the following scores: 50, 62, 80, 75, and 70. What test score must Mark earn on his sixth test so that his average (mean score) for all six tests will be 60? 10. For what value of n will 5, 9 and n have the same mean (average) as that of 16 and 24?

21 Topic : Central Tendency - Mean, Mode, Median - Worksheet 2 Marcy consumes 1.1, 2.1, 2.3, 2.1, 1.8, 2.5, 1.5, and 2.4 grams of cake respectively in a week. Find the following measures of central tendency based on Marcy s data: 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Prepare a frequency distribution with a class interval of 0.4 for the above data set. Cake amount Frequency Find the modal interval. 6. What would be the average if she consumes 0.4 g more cake every day? 7. What would be the mode if she consumes 0.3 g more cake every day? 8. For what value of n will 9, 3 and n have the same mean (average) as that of 6 and 4? 9. On his first 4 science tests, Rick received the following scores: 35, 55, 70 and 75. What test score must Rick earn on his fifth test so that his average (mean score) for all five tests will be 50? 10. For what value of n will 6, 8 and n have the same mean (average) as that of 12 and 8?

22 Topic : Central Tendency - Mean, Mode, Median - Worksheet 3 Joshua consumes 2, 3, 5, 4, 8, 3, 3, and 6 grams of rice in a week. Find the following measures of central tendency based on Joshua s data: 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Prepare a frequency distribution with a class interval of 3 for the above data set. Rice amount 2-4 Frequency Find the modal interval. 6. What would be the average if he consumes 0.5 g more Rice every day? 7. What would be the mode if he consumes 0.4 g more Rice every day? 8. For what value of y will 5, 7 and y have the same mean (average) as that of 9 and 7? 9. On her first 5 biology tests, Jenny received the following scores: 50, 60, 75, 80, and 55. What test score must Jenny earn on her sixth test so that her average (mean score) for all six tests will be a 60? 10. For what value of m will 4, 8 and m have the same mean (average) as that of 10 and 18?

23 Topic : Central Tendency - Mean, Mode, Median - Worksheet 4 Ricky consumes 4, 2, 6, 4, 5, 4, 7, and 8 grams of tea in a week. Find the following measures of central tendency based on Ricky s data: 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Prepare a frequency distribution with a class interval of 3 for the above data set. Tea amount 2-4 Frequency Find the modal interval. 6. What would be the average if he consumes 0.2 g more Tea every day? 7. What would be the mode if he consumes 0.1 g more Tea every day? 8. For what value of x will 8, 6 and x have the same mean (average) as that of 8 and 12? 9. On his first 5 history tests, Tom received the following scores: 30, 45, 85, 60 and 70. What test score must Tom earn on his sixth test so that his average (mean score) for all sixth tests will be 40? 10. For what value of m will 6, 4 and m have the same mean (average) as that of 14 and 16?

24 Topic : Central Tendency - Mean, Mode, Median - Worksheet 5 Mark consumes 3, 8, 4, 6, 7, 9, 5, and 6 grams of pizza in a week. Find the following measures of central tendency based on Mark s data: 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Prepare a frequency distribution with a class interval of 3 for the above data set. Pizza amount 1-3 Frequency Find the modal interval. 6. What would be the average if he consumes 0.5 g more pizza every day? 7. What would be the mode if he consumes 1 gram more Pizza every day? 8. For what value of n will 2, 8 and n have the same mean (average) as that of 12 and 18? 9. On his first 4 English tests, Paul received the following scores: 55, 60, 35 and 90. What test score must Paul earn on his fifth test so that his average (mean score) for all five tests will be 50? 10. For what value of y will 8, 6 and y have the same mean (average) as that of 20 and 10?