Basic Mean median mode Standard Deviation
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The document provides information about calculating the mean, median, mode, range, variance, and standard deviation of a data set of test scores for nine vocational technical students. It gives the definitions and step-by-step processes for finding each measure. As an example, it calculates the mean as 87, the median as 88, the mode as 97, and the range as 34 for the data set of test scores {63, 73, 84, 86, 88, 95, 97, 97, 100}. It then works through calculating the variance as 135.1 and the standard deviation as 11.6 for this same data set.
Basic Mean median mode Standard Deviation
- 2. These are Voc Tech Students test scores. 97 84 73 88 100 63 97 95 86
- 3. What can you tell us about these numbers? 97 84 73 88 100 63 97 95 86
- 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.
- 6. Lets find Students of Voc Tech MEAN test score? 97 84 73 88 100 63 97 95 86 + 783 783 ÷ 9 The mean is 87
- 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.
- 8. 978473 88 10063 979586 The median is 88. Half the numbers are less than the median. Half the numbers are greater than the median.
- 9. Median Sounds like MEDIUM Think middle when you hear median.
- 10. How do we find the MEDIAN when two numbers are in the middle? 1. Add the two numbers. 2. Then divide by 2.
- 11. 978473 88 10063 9795 88 + 95 = 183 183 ÷ 2 The median is 91.5
- 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
- 13. 978473 88 10063 979586 The value 97 appears twice. All other numbers appear just once. 97 is the MODE
- 14. A Hint for remembering the MODE… The first two letters give you a hint… MOde Most Often
- 15. What is the RANGE? How do we find it? The RANGE is the difference between the lowest and highest values.
- 16. 978473 8863 979586 97 -63 34 34 is the RANGE or spread of this set of data
- 17. This one is the requires more work than the others. Right in the MIDDLE. This one is the easiest to find— Just LOOK.
- 18. Find the….
- 20. Find the….
- 22. Find the….
- 24. Find the….
- 27. • Variance is the average squared deviation from the mean of a set of data. It is used to find the standard deviation. Variance
- 28. 1. Find the mean of the data. Hint – mean is the average so add up the values and divide by the number of items. 2. Subtract the mean from each value – the result is called the deviation from the mean. 3. Square each deviation of the mean. 4. Find the sum of the squares. 5. Divide the total by the number of items. 6.Take the square root of the variance – result is the standard deviation.
- 29. Variance Formula • The variance formula includes the Sigma Notation, , which represents ∑ the sum of all the items to the right of Sigma. ∑(x−µ)2 n Mean is represented by and µ n is the number of items.
- 30. Standard Deviation • Standard Deviation shows the variation in data. If the data is close together, the standard deviation will be small. If the data is spread out, the standard deviation will be large. • Standard Deviation is often denoted by the lowercase Greek letter σ sigma, .
- 31. Standard Deviation • Find the variance. • Find the mean of the data. • Subtract the mean from each value. • Square each deviation of the mean. • Find the sum of the squares. • Divide the total by the number of items. • Take the square root of the variance.
- 32. Standard Deviation Formula • Notice the standard deviation formula is the square root of the variance. The standard deviation formula can be represented using Sigma Notation: σ= ∑(x−µ)2 n
- 33. 2. Find the variance and standard deviation • The test scores of nine voctech students are: 63,73,84,86,88,95,97,97,100 1. Find the mean: (63,73,84,86,88,95,97,97,100)and /9=87.
- 34. Find the deviation from the mean: 63-87=-24 97-87=10 73-87=-14 97-87=10 84-87=-3 100-87=13 86-87=-1 88-87=1 95-87=8
- 35. 3. Square the deviation from the mean:
- 36. 4. Find the sum of the squares of the deviation from the mean: 576+196+9+1+1+64+100+100+169= 1216
- 37. 5. Divide by the number of data items to find the variance: 1216 9 = 135.1 - 135.1
- 38. 6. ) Find the square root of the variance: 135.1 = 11.6 Thus the standard deviation of the test scores is 11.6
- 39. Thank you very much muwah