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Percentiles Measures of central tendency that divide a group of data into 100 parts. At least n% of the data lie below the nth percentile, and at most (100 - n)% of the data lie above the nth percentile. Example: 90th percentile indicates that at least 90% of the data lie below it, and at most 10% of the data lie above it. The median and the 50th percentile have the same value. BIC Prepaid By:Rajyagor Bhargav

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Percentiles: Computational Procedure Organize the data into an ascending ordered array. Calculate the percentile location: Determine the percentile’s location and its value. If i is a whole number, the percentile is the average of the values at the i and (i+1) positions. If i is not a whole number, the percentile is at the (i+1) position in the ordered array. BIC Prepaid By:Rajyagor Bhargav

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Percentiles: Example Raw Data: 14, 12, 19, 23, 5, 13, 28, 17 Ordered Array: 5, 12, 13, 14, 17, 19, 23, 28 Location of 30th percentile: The location index, i, is not a whole number; i+1 = 2.4+1=3.4; the whole number portion is 3; the 30th percentile is at the 3rd location of the array; the 30th percentile is 13. BIC Prepaid By:Rajyagor Bhargav

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Quartiles Measures of central tendency that divide a group of data into four subgroups. Q 1 : 25% of the data set is below the first quartile Q 2 : 50% of the data set is below the second quartile Q 3 : 75% of the data set is below the third quartile Q 1 is equal to the 25th percentile Q 2 is located at 50th percentile and equals the median Q 3 is equal to the 75th percentile Quartile values are not necessarily members of the data set BIC Prepaid By:Rajyagor Bhargav

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Quartiles 25% Q3Q3 Q2Q2 Q1Q1 BIC Prepaid By:Rajyagor Bhargav

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Quartiles: Example Ordered array: 106, 109, 114, 116, 121, 122, 125, 129 Q 1 Q 2 : Q 3 : BIC Prepaid By:Rajyagor Bhargav

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Range(useful measure of Dispersion) Dispersion may be measured in term of the distance between two values selected from the data set. BIC Prepaid By:Rajyagor Bhargav

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Range Range is the difference between the highest and lowest observed values. In equation we can say Range = value of highestvalue of lowest observation BIC Prepaid By:Rajyagor Bhargav

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Defining and computing the range Annual payment for a company (‘000) A863903957104111381204 135416241698174518021883 B490540560570590600 610620630660670690 Range for annual payment for company A is 1883000-863000=1020000 B is 690000-490000=200000 BIC Prepaid By:Rajyagor Bhargav

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Characteristics The range is easy to understand and to find. It consider only the highest and lowest value of a distribution and fails to take account of any other observation in dataset. It is heavily influenced by extreme values, because it measures only two values. Open end distribution have no range. BIC Prepaid By:Rajyagor Bhargav

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Interquartile Range Range of values between the first and third quartiles Range of the “middle half” Less influenced by extremes BIC Prepaid By:Rajyagor Bhargav

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Compute the inter quartile range It measures the approximately how far from the median. we must go on the either side before we can include one half the values of the dataset. To compute this range we divide our data into 4 parts, each of which contains 25% of items in the distribution. BIC Prepaid By:Rajyagor Bhargav

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The quartile are then the highest value in each of these four part. Inter quartile range is the difference between the values of the first and third quartile: Inter Quartile range : =Q3 - Q1 Inter quartile range BIC Prepaid By:Rajyagor Bhargav

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Exercise (Ex.3.56) 0.1 0.450.5 0.32 0.89 1.20.530.670.58 0.48 0.23 0.77 0.12 0.66 0.59 0.95 1.1 0.83 0.69 0.51 Find range and Inter Quartile Range BIC Prepaid By:Rajyagor Bhargav

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