Introduction to StatisticsCh-3:Measures of Central TendencyModeModeModeIt is a value of a particular type of items which occur most frequently.Ungrouped (individual series)cases: The value appearing mostfrequently (the most frequent value) is taken as the modal value.Examples: Find the mode of the following data sets.1. 110, 113, 116, 116, 118, 118, 118, 121 and 123.2. 2, 3, 5, 7 and 8.3. 15, 18, 18, 18, 20, 22, 24, 24, 24, 26 and 26.4. 5, 6, 6, 7, 9, 9, 10, 12 and 12.5. 1, 1, 0, 1, 0, 0, 0, 2, 4 and 3.73 / 159Introduction to StatisticsCh-3:Measures of Central TendencyModeSolutions1. Since 118 occurs more than other values, the mode is 118.2. Each value occurs once (equally frequent), the data has no mode.3. 18 and 24 occur three times, hence the modal values are 18 and 24(bi-modal).4. Tri-modal (multi-modal): 6, 9 and 12.5. The modal value here is 0 as it occurs more number of times than othervalues.74 / 159Introduction to StatisticsCh-3:Measures of Central TendencyModeMode - Contd.Grouped (continuous) series: In a grouped frequency distribution, themodal value is located in the class with highest frequency and that classis the modal class.ˆX=LˆX+fˆX-fˆX-1(fˆX-fˆX-1) + (fˆX-fˆX+1)×wExample: Find the modal score of the students score data.The class having highest frequency is⇒26.5-30.5, hence it is the modalclass.ˆX= 26.5 +12-10(12-10) + (12-7)×4 = 26.5 + 1.14 = 27.6475 / 159Introduction to StatisticsCh-4:Measures of VariationDefinition of VariationWhat is Variation?Example: Find the mean and median prices of the four cities andinterpret it.A3030303030B2829303132C1015304550D05305560Are all the four data sets the same?If yes, why?If no, why not?VariationVariation (dispersion) may be defined as the extent of scatteredness of valuearound the measures of central tendency.76 / 159