stands for the mean deviation from median,Myfor the total of the values above theactual median, and Mxfor the values below it, and N for the number of items. δ´X=1N(´X y−´X x)Where δ´Xstand for the mean deviation from mean, ´X ystands for the total of the values abovethe actual arithmetic average and ´X xfor the values below it. Example 8The following are the marks obtained by a batch of 9 students in a certain test:Sl. No.Marks (out of 100)Sl. No.Marks (out of 100)168638249759332866421941554Calculate mean deviation of the series from median.
(Answer: Mean Deviation = 12.8 marks)SolutionDirect MethodCalculation of mean deviation of the series of marks of 9 students (arranged in ascending order ofmagnitude)Marks (out of100)Deviations from Median (49)(X)(+, - sign ignored)212832173811418490545591066176819∑∣dM∣= 115Median = the value of (N+12)thitem = 49Mean Deviation, δM=∑∣dM∣NWhere, ∑∣dM∣represents the summation of he deviations from the median and N, the number ofitemsδM=1159=12.8MarksShort cut Method Marks arranged in ascending order of magnitude
Sum of items above median (with values less than median)= 21+32+38+41 = 132 (Mx)Sum of items below median (with values more than median)= 54+59+66+68 = 247 (My)δM=1N(My−Mx)δM=19(247−132)= 12.8 MarksPractice Example 9Calculate Mean Deviation (from arithmetic Average) for the following values. Also, calculate its Coefficient. 4800, 4600, 4400, 4200, 4000. (Answer: Mean Deviation = 240, Co-efficient of Mean Deviation = 0.54)Practice Example 10Calculate mean deviation (from arithmetic Average) for the following values.100.500100.250100.375100.625100.750100.125100.375100.625100.500100.125(Answer: Mean Deviation = 0.175)Calculation of mean deviation in Discrete SeriesExample 11Find the mean deviation of the distribution given belowNo. ofAccidentsPersons having saidno. of AccidentsNo. ofAccidentsPersons having saidno. of Accidents0157211681221923101024171105812264(Answer: Mean deviation from Median is 1.96 accidents)
SolutionNo. of AccidentsPersons havingsaid no. ofAccidentsCumulativeNumber ofAccidentsDeviation fromMedian (2)(+, - signs ignored)TotalDeviations(X)(f)(dM)(fdM)01515230116311162215200310621104177923458873246491416729351081946692967141029881611098901221001020N = 100 ∑∣fdM∣=196Mean Deviation δM=∑∣dM∣N=196100=1.96accidentsPractice Example 12Calculate the mean deviation (from mean) of the following series:MarksNo. of Students5515825153516456(Answer: mean deviation 9.44 marks)(Hint: calculate mean by step deviation, further find mean deviation from mean)Calculation of Mean Deviation in Continuous Series
Example 13Calculate the mean deviation (from median) from the following dataClass IntervalFrequencyClass IntervalFrequency1-369-11213-55311-13165-78513-1547-95615-174(Answer: mean deviation is 2.1)(Hint: Refer Example 25 from Measures of Central Tendency for Mean)SolutionClass IntervalMid-PointDeviation fromActual Median FrequencyDev * fDev fromAssumedDev * f1-363-5535-7857-9569-112111-131613-15415-174TotalDirect Method______________________________________________________________________________________________________________________________________________________________________