Mean median & mode statistics
- 1. Ishfaq-Arif (BSSE) COMSATS INSTITUTE OF TECHNOLOGY VEHARI CAMPUS 10/5/2016 4:54:57PM 1
- 2. Mean: SUMMING UP ALL THE OBSERVATION AND DIVIDING BY NUMBER OF OBSERVATIONS. MEAN OF 20, 30, 40 IS (20+30+40)/3 = 30. n x n xxx x x nxxx n i i n n 121 ,21 ... variable,thisofmeanThen the. variableaofnsobservatioare...,Let:Notation 10/5/2016 4:54:57PM 2
- 4. The middle value in an ordered sequence of observations. That is, to find the median we need to order the data set and then find the middle value. In case of an even number of observations the average of the two middle most values is the median. For example, to find the median of {9, 3, 6, 7, 5}, we first sort the data giving {3, 5, 6, 7, 9}, then choose the middle value 6. If the number of observations is even, e.g., {9, 3, 6, 7, 5, 2}, then the median is the average of the two middle values from the sorted sequence, in this case, (5 + 6) / 2 = 5.5. MEDIAN: (MIDDLE) 10/5/2016 4:54:57PM 4
- 5. Examples : Odd Number of Elements Data Set = 2, 5, 9, 3, 5, 4, 7 Reordered = 2, 3, 4, 5, 6, 7, 9 ^ Median = 5 10/5/2016 4:54:57PM 5
- 6. Examples : Even Number of Elements Data Set = 2, 5, 9, 3, 5, 4 Reordered = 2, 3, 4, 5, 5, 9 ^ ^ Median = ( 4 + 5 ) / 2 = 4.5 10/5/2016 4:54:57PM 6
- 7. Mode : (most often) The "Mode" for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. This happens when two or more elements occur with equal frequency in the data set. 10/5/2016 4:54:57PM 7
- 8. Examples a) 5.40 1.10 0.42 0.73 0.48 1.10 b) 27 27 27 55 55 55 88 88 99 c) 1 2 3 6 7 8 9 10 Mode is 1.10 Bimodal - 27 & 55 No Mode 10/5/2016 4:54 PM 8