 # The median value for grouped frequency distributions

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The median value for grouped frequency distributions is given by theformula:˜X=L˜X+n2-F˜X-1f˜X×wwheren=ki=1fiis the total number of observations,f˜
70 / 159Introduction to StatisticsCh-3:Measures of Central TendencyMedian and QuantilesMedian - Contd.Example: Find the median mark of the students score data and interpretit.Introduction to StatisticsCh-3:Measures of Central TendencyMedian and QuantilesSolutions - Contd.
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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 is26.5-30.5, 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
Introduction to StatisticsCh-4:Measures of VariationDefinition of VariationObjectives of Measures of Variation1.To have an idea about the reliability of the measures of centraltendency. If the degree of scatterdness is large, an average is lessreliable.

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