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Calculation of Median
- 1. Calculation of Median SUBMITTED BY DR.SUNITA OJHA ASSISTANT PROFESSOR SURESH GYAN VIHAR UNIVERSITY
- 2. Median • The medianis usually defined as that value which divides a distribution so that equal number of items occur on either side of it. • In other words 50 percent of the observations will be smaller than the median and 50 percent of the observations will be greater than the median. 1. Calculation of median in a series of individual observations: • Arrange the data in the ascending or descending order • Median is located by finding the size of the (n+1/2)th item. 𝑴 = 𝒏 + 𝟏 𝟐 𝒕𝒉 𝒊𝒕𝒆𝒎 M= Median n= number of observations Example 1. Find out the median from the data recorded on the number of clusters per plant in a pulse crop: 10,18, 17, 19, 10, 15, 11, 17, 12
- 3. S. No. Dataarranged in ascending order 1 10 2 10 3 11 4 12 5 15 6 17 7 17 8 18 9 19 Median = Size of (n+1)/2 th item = (9+1)2 th item =5th item Median = 15 2. Calculation of median in a discrete series • Data should be arranged in ascending or descending order of magnitude • Find out the cumulative frequencies • Median= size of the (n+1)/2 th item • Find out the (n+1)/2 th item. It can be found by first locating the cumulative frequency which is equal to (n+1)/2 or the next higher to this and then determine the value corresponding to it. This will be the value of median.
- 4. Example 1. Findout the median of the following data No. of angular seeded plants 12 8 17 10 11 16 18 14 6 7 No. of plants 39 33 42 40 47 42 60 50 22 25 No. of angular seeded plants No. of plants Cumulative Frequency 6 22 22 7 25 47 8 33 80 10 40 120 11 47 167 12 39 206 14 50 256 16 42 298 17 42 340 18 60 400 Median = (400+1)/2 th item =200.5th item Median=12
- 5. 3. Calculation ofmedian in a continuous series • While computing the value of the median in a continuous series, first determine the particular class in which the value of the median lies. • Use n/2 as the rankof the median and not (n+1)/2 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 L= lower limit of the median class cf= cumulative frequency of the class preceding the median class f=frequency of the median class i= class interval
- 6. No. of grainsper earhead classes Frequency Cumulative frequency 5-10 2 2 10-15 27 29 15-20 52 81 20-25 118 199 25-30 57 256 30-35 27 283 35-40 13 296 40-45 4 300 Example 1. Calculate the value of the median from the data recorded on the number of grains per earhead on 300 wheat earhead. Solution: Median= Size of (n/2)th item= 300/2= 150 Median lies in the class=20-25 L=20; n/2= 150; cf=81; i=5; f=118 Median=20+(69/118)*5 =20+2.92 =22.92
- 7. 4. Calculation ofmedian in unequal class- intervals • In unequal class-interval frequencies need not be adjusted to make the class intervals equal and the formula can be used here. 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 n/2=70/2= 35 Median= 30+ ((35-21)/10)*10 = 30+(140/10)*10 =30+14 =44 Classes Frequency Cumulative Frequency 0-10 5 5 10-30 16 21 30-60 30 51 60-80 12 63 80-90 6 69 90-100 1 70 Classes Frequency Cumulative Frequency 0-10 5 5 10-20 8 13 20-30 8 21 30-40 10 31 40-50 10 41 50-60 10 51 60-70 6 57 70-80 6 63 80-90 6 69 90-100 1 70
- 8. 5. Calculation ofmedian in open-end classes • Since the median is not affected by the values of extreme ends we are not concerned with the extreme values for the calculation of median in open-end classes. Size of item classes Frequency Cumulative Frequency Less than 10 4 4 10-20 8 12 20-30 14 26 30-40 6 32 40 and above 4 36 Example 1. Calculate the median in open –end series. Solution: 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 n/2= 36/2= 18th item Median lies in the class 20-30 Median= 20+((18-12)/14)*10 =24.29
- 9. 6. Graphic Locationof Median: • Draw two ogives one by less than method and the other by more than method. • From the point where the two curves intersect draw a perpendicular line to the X- axis. The point on the X-axis will give the median value.