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

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

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

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

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

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

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

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

Defining and computing the range Annual payment for a company (‘000) A B  Range for annual payment for company  A is =  B is = BIC Prepaid By:Rajyagor Bhargav

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

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

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

 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

Exercise  (Ex.3.56)   Find range and Inter Quartile Range BIC Prepaid By:Rajyagor Bhargav