1. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam WFM 5201: Data Management and Statistical Analysis Akm Saiful Islam Lecture-2: Descriptive Statistics [Measures of Location] April, 2008 Institute of Water and Flood Management (IWFM) Bangladesh University of Engineering and Technology (BUET)

2. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Descriptive Statistics Measures of Central Tendency Measures of Location Measures of Dispersion Measures of Symmetry Measures of Peakdness

3. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Measures of Location Measures that are allied to the median include the quartiles, deciles and percentiles, because they are also based on their position in a series of observations. These measures are referred to as measures of location and not the measures of central tendency as they describe the position of one score relative to the others rather than the whole set of data.

4. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Measures of Location Quartile  One fourth (1/4) First (1/4), Second (1/2), Third (3/4) Decile  One tenth (1/10) 10%, 20%, …90% Percentile  One of hundreds (1/100) 1%, 2%, ….99%

5. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Quartile L 0 = Lower limit of the i-th Quartile class n = Total number of observations in the distribution h = Class width of the i-th Quartile class f i = Frequency of the i-th Quartile class F = Cumulative frequency of the class prior to the i-th quartile class

6. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Decile L 0 = Lower limit of the i-th Decile class n = Total number of observations in the distribution h = Class width of the i-th Decile class f i = Frequency of the i-th Decile class F = Cumulative frequency of the class prior to the i-th Decile class

7. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Percentile L 0 = Lower limit of the i-th Percentile class n = Total number of observations in the distribution h = Class width of the i-th Percentile class f i = Frequency of the i-th Percentile class F = Cumulative frequency of the class prior to the i-th Percentile class

8. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Example-1: Percentile of Ungroup data Consider the observations 11, 14, 17, 23, 27, 32, 40, 49, 54, 59, 71 and 80. To determine the 29th percentile? we note that which is not an integer. Thus the next higher integer 4 here will determine the 29th percentile value. On inspection P 29 = 23

9. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Example-2: Find 3 rd Quartiles, 1 st Decile and 29 th Percentile MarksNo. of studentsCumulative frequencies 40-5066 50-601117 60-701936 70-801753 80-901366 90-100470 Total70

10. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Example-3: Find 30 th percentile Age in yearsNumber of birthsCumulative number of births 14.5-19.5677 19.5-24.519082585 24.5-29.517374332 29.5-34.510405362 34.5-39.52945656 39.5-44.5915747 44.5-49.5165763 All ages5763-

11. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam Determine Percentile Class First determine the percentile class. If, N =5736, and we have to find 30 th percentile, then percentile class will be the class which has cumulative frequency below:

12. WFM 5201: Data Management and Statistical Analysis © Dr. Akm Saiful IslamDr. Akm Saiful Islam 30 th Percentile class Age in yearsNumber of birthsCumulative number of births 14.5-19.5677 19.5-24.519082585 24.5-29.517374332 29.5-34.510405362 34.5-39.52945656 39.5-44.5915747 44.5-49.5165763 All ages5763- 1728.9