Unit 1 BP801T a introduction mean median mode
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This document provides information and examples for calculating various statistical measures - mean, median, mode, range - from data sets. It explains that the mean is the average found by adding all values and dividing by the number of values, the median is the middle number of a data set arranged in order, and the mode is the most frequently occurring value. Examples are given to demonstrate calculating each measure from sets of test score data. Frequency and cumulative frequency are also defined.
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Here are the steps to calculate the standard deviation of {10, 12, 23, 45, 120} by hand:
1) Find the mean: 10 + 12 + 23 + 45 + 120 = 210. The mean is 210/5 = 42
2) Subtract the mean from each value:
10 - 42 = -32
12 - 42 = -30
23 - 42 = -19
45 - 42 = 3
120 - 42 = 78
3) Square the differences: (-32)2 = 1024, (-30)2 = 900, (-19)2 = 361, 32 = 9, 782 = 6084
4) Sum the squared differences: 1024 + 900 +
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Unit 1 BP801T a introduction mean median mode
- 1. 1
- 2. These are Abby’s science test scores. 97 84 73 88 100 63 97 95 86 2
- 3. What can you tell us about these numbers? 97 84 73 88 100 63 97 95 86 3
- 4. 4
- 5. What is the MEAN? How do we find it? The mean is the numerical average of the data set. The mean is found by adding all the values in the set, then dividing the sum by the number of values. 5
- 6. Lets find Abby’s MEAN science test score? 97 84 73 88 100 63 97 95 86 + 783 783 ÷ 9 The mean is 87 6
- 7. What is the MEDIAN? How do we find it? The MEDIAN is the number that is in the middle of a set of data 1. Arrange the numbers in the set in order from least to greatest. 2. Then find the number that is in the middle. 7
- 8. 97 84 73 88 100 63 97 95 86 The median is 88. Half the numbers are less than the median. Half the numbers are greater than the median. 8
- 9. Median Sounds like MEDIUM Think middle when you hear median. 9
- 10. How do we find the MEDIAN when two numbers are in the middle? 1. Add the two numbers. 2. Then divide by 2. 10
- 11. 97 84 73 88 100 63 97 95 88 + 95 = 183 183 ÷ 2 The median is 91.5 11
- 12. What is the MODE? How do we find it? The MODE is the piece of data that occurs most frequently in the data set. A set of data can have: • One mode • More than one mode • No mode 12
- 13. 97 84 73 88 100 63 97 95 86 The value 97 appears twice. All other numbers appear just once. 97 is the MODE 13
- 14. A Hint for remembering the MODE… The first two letters give you a hint… MOde Most Often 14
- 15. Which set of data has ONE MODE? 9, 11, 16, 8, 16 9, 11, 16, 6, 7, 17, 18 18, 7, 10, 7, 18 A C B 15
- 16. Which set of data has NO MODE? 13, 12, 12, 11, 12 9, 11, 16, 6, 7, 17, 18 18, 7, 10, 7, 18 A C B 16
- 17. Which set of data has MORE THAN ONE MODE? 9, 11, 16, 8, 16 9, 11, 16, 6, 7, 17, 18 18, 7, 10, 7, 18 A C B 17
- 18. What is the RANGE? How do we find it? The RANGE is the difference between the lowest and highest values. 18
- 19. 97 84 73 88 63 97 95 86 97 -63 34 34 is the RANGE or spread of this set of data 19
- 20. What is the RANGE of this set of data? 84 71 88 99 48 97 86 20
- 21. What is the RANGE of this set of data? 84 71 88 99 48 97 86 99 -48 51 21
- 22. What is the RANGE of this set of data? 33 67 85 17 48 15 46 22
- 23. What is the RANGE of this set of data? 85 -15 70 33 67 85 17 48 15 46 23
- 24. What is the RANGE of this set of data? 267 119 357 401 329 483 227 24
- 25. What is the RANGE of this set of data? 267 119 357 401 329 483 227 483 -119 364 25
- 26. This one is the requires more work than the others. Right in the MIDDLE. This one is the easiest to find— Just LOOK. 26
- 27. Find the…. 27
- 28. 28
- 29. Find the…. 29
- 30. 30
- 31. Find the…. 31
- 32. 32
- 33. Find the…. 33
- 34. 34
- 35. Find the…. 35
- 36. 36
- 37. FREQUENCY: A frequency is the number of times a data value occurs. For example, if ten students score 80 in statistics, then the score of 80 has a frequency of 10. Frequency is often represented by the letter f. A frequency chart is made by arranging data values in ascending order of magnitude along with their frequencies. 37
- 38. CUMULATIVE FREQUENCY Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. 38