This is 638004274-MEASURES-OF-VARIABILITY.pptx

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1. MEASURES OF VARIABILITY *Measures of variability, range, variance, standard deviation centile deviations *Computation and interpretation of measures from grouped data

2. What is Variability? Refers to how “spread out” a group of scores is. Is the measure of the spread of a data set In other words, variability measures how much your scores differ from each other. Variable - Any entity that can take on different values.

3. Four Measure of Variability Range Standard Deviation Variance

4. RANGE Is simply the highest score/value minus the lowest score/value in the set. Example: Given the following data, find the range. 12, 15, 19, 24, 25, 26, 30, 35, 38 R= HV-LV R= 38- 12 R=26

5. STANDARD DEVIATION It is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

6. There are six steps for finding the standard deviation by hand: List each score and  find their mean . Subtract the mean from each score to get the deviation from the mean. Square each of these deviations. Add up all of the squared deviations. Divide the sum of the squared deviations by  n  – 1 (for a  sample ) or  N  (for a population). Find the square root of the number you found.

7. What is Mean? The  mean  is the average of a data set It provides a measure of central location of the data How to find the mean, Look at your data set. Add the numbers in your sample together. Divide the sum by how many numbers are there in your sample.

8. VARIANCE is the square of the standard deviation. it refers to a statistical measurement of the spread between numbers in a data set and measures how far each number in the set is from the mean and thus from every other number in the set.

9. Problem: 1. The weights, in pounds, of dogs in a group are: 25, 83, 15, 30, 17, 72, 40, 32, 19. Find: Range Variance Standard Deviation Round to two decimal places.

10.  Order the data from smallest to largest. 15, 17, 19, 25, 30, 32, 40, 72, 83. The range is the largest value minus the smallest value. 83 - 15 = 68. The mean is (15 + 17 + 19 + 25 + 30 + 32 + 40 + 72 + 83) / 9 = 333 / 9 = 37. Find the difference between each weight and the mean and square the results

11. Add these results and divide by 9 to get the variance. (484 + 400 + 324 + 144 + 49 + 25 + 9 + 1225 + 2116) / 9 = 4776 / 9 = 530.67 The standard deviation is the square root of the variance.

12. THANK YOU