Week-8-Measures-of-Variation pptx mathem

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1. M EASURES of V ARIATION RANGE VARIANCE STANDARD DEVIATION Mr. Armando U. Miranda Jr., MATM 111 Instructor

2. Events of nature vary from time. People keep on changing their location, motion, physical appearance, skin reaction to different chemicals, height, weight, hair color, eye color, ideas, and even value in life. Usually, the heights of a group of people with the same race tend to converge to a certain common value.

3. MEASURES OF VARIATION The measures of variation will enable you to know how varied the observations are, whether there are extremes values in the distribution, or whether the values are very close to each other. If the measure of variation is zero, it means that there is no variation at all and that the observations are all alike, or homogeneous. Otherwise, they are heterogenous . The common measures of variations are: range, variance , and standard deviation other measures of variation: mean absolute deviation, interquartile range, quartile deviation

4.  The range is simple to compute and is useful when you wish to evaluate the whole of a dataset. The range is useful for showing the spread within a dataset and for comparing the spread between similar datasets. FORMULA: Range (R) = HIGHEST OBSERVATION – LOWEST OBSERVATION is the simplest form of measuring the variation of a distribution.

5. Illustrative Examples: Data 3: A group of scientists went on the mountain range in Sierra Madre, Philippines to study the different species of plants existing in that area. The ages of the scientists are 34, 35, 45, 56, 32, 25, and 40. What is the range of their ages? Given : Highest Age = 56 and Lowest Age = 25 Solution : R = H – L = 56 – 25 = 31 Answer: therefore, the range of their ages is 31

6. VARIANCE Variance is another measure of variation which can be used instead of the range. The variance considers the deviation of each observation from the mean. To obtain the variance of a distribution, first square the deviation from the mean of each row score and add them together. Then, divide the resulting sum by N or the total number of cases.

7. (Ungrouped Data) (Ungrouped Data)

8. (Ungrouped Data) (Grouped Data) Except when specified that the population variance is to be used, you will always use the sample variance formula in the examples and exercises.

9. x 34 35 45 56 32 25 40 N = 7 x 34 35 45 56 32 25 40 N = 7 x 34 35 45 56 32 25 40 N = 7 x 34 35 45 56 32 25 40 N = 7 x 34 17.14 35 9.86 45 47.06 56 318.98 32 37.70 25 172.66 40 3.46 N = 7 606.86 x 34 17.14 35 9.86 45 47.06 56 318.98 32 37.70 25 172.66 40 3.46 N = 7 606.86  

10. (Ungrouped Data) (Grouped Data)

11. The standard deviation, (σ ) for a population and (s) for a sample, is the square root of the value of the variance. In symbols and formula for grouped and ungrouped data:

12.   Ungrouped Data: If the Population Variance is , therefore , the value of population standard deviation is Ungrouped Data: If the Sample Variance is , therefore , the value of sample standard deviation is     This means that the formula in finding the standard deviation is: , population SD , for sample SD  

13. What questions do you have in mind? If there’s none, prepare for your asynchronous learning.