8/3/2019 Calculation of Median

1/12

Calculation of Median

Individual series

Formula :Median = Size of N+1 th item

2

Steps :1.Arrange the data is ascending or descendingOrder.2.Apply Formula

8/3/2019 Calculation of Median

2/12

QQ.. From the following data of the wages of 7From the following data of the wages of 7workers compute the median.workers compute the median.

WWages ( in Rs.) 1100 1150 1080 1120 1200 1160 1400

For even no. of itemsITEMS : 3 8 6 4 2 5 7 9 11 7

8/3/2019 Calculation of Median

3/12

Calculation of Median

Discrete SeriesFormula :

Median = Size of N+1 th item

2STEPS :1.Arrange the data is ascending or descending

Order.

2. Find out the cumulative Frequencies3.Apply Formula4. Now look at the Cumulative frequency column and

find the total which is either equal to N+1 or nexthigher to it . That

5. gives the value of median 2

8/3/2019 Calculation of Median

4/12

Income(in Rs.) : 1000 1500 800 2000 2500 1800

No. ofPersons : 24 26 16 20 6 30

Ans : 1500Q.Calculate the Median from the followingfrequency distribution.

Marks : 5 10 15 20 25 30 35 40 45 50

Students :20 43 75 76 72 45 39 9 8 6Med : 20

8/3/2019 Calculation of Median

5/12

CalCalculation of Median Continuous Series

Median Size= N/2 th item

Median = L + N/2 - c . fX i

fL = Lower limit of median class

c. f = Cumulative frquency of the class precedingmedian class

f = frequency of median classi = class interval of median class

8/3/2019 Calculation of Median

6/12

Q. Calculate the median for the following distribution

45-50 1040-45 15

35-40 2630-35 3025-30 4220-25 31

15-20 2410-15 155-10 7

8/3/2019 Calculation of Median

7/12

Value Frequency Value FrequencyLess than 10 4Less than 10 4

Less than 20 16Less than 20 16Less than 30 40Less than 30 40Less than 40 76Less than 40 76Less than 50 96Less than 50 96

Less than 60 112Less than 60 112Less than 70 120Less than 70 120Less than 80 125Less than 80 125

Sol : Since the lower limit of frequency is not defined ,Sol : Since the lower limit of frequency is not defined ,

therefore frequencies are cumulative.therefore frequencies are cumulative.Ans : 36.95Ans : 36.95

8/3/2019 Calculation of Median

8/12

Q. Compute Median from the followingData .

Mid Value Frequency115 6

125 25

135 48145 72155 116165 60175 38

185 22195 3

Ans : 153.79

8/3/2019 Calculation of Median

9/12

Q. Find the missing Frequency from the

following distribution if N is 100 and medianis 30Marks No. of students

0-10 1010-20 ?20-30 2530-40 30

40-50 ?50-60 10

Ans : 15,10

8/3/2019 Calculation of Median

10/12

Calculate the Median from followingCalculate the Median from followingData.Data.Marks : 0Marks : 0--10 1010 10--30 3030 30--60 6060 60--80 8080 80--9090Frequency : 5 15 30 8 2Frequency : 5 15 30 8 2

Ans : 40Ans : 40

8/3/2019 Calculation of Median

11/12

Q. Computation ofQuartiles , DecilesQ. Computation ofQuartiles , DecilesPercentiles , etc.Percentiles , etc.

QuartileQuartile :: That value which divides theThat value which divides theseries into four equal parts , There are threeseries into four equal parts , There are threepointspointsDecilesDeciles : That value which divides theseries into 10 equal parts. There are 9pointsPercentile : That value which divides the

series into 100 equal parts. There are 99points

8/3/2019 Calculation of Median

12/12

For individual and Discrete SeriesQ1 = Size of N+1 th item

4Q2 = second Quartile = medianQ3 = Size of 3(N+1) th item

4For Continuous SeriesQ1 = Size of N th item

4

Q2 = second Quartile = medianQ3 = Size of 3N th item

4