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Measurement of Dispersion

Measurement of Dispersion

 

Central tendency gives the single central value in distribution which cannot gives us information about spread, scatter or variability of individual item. So dispersion is an important measure for describing the character of variability in data and its help to determine the reliability of an average. Dispersion may be either absolute or relative which can be measure as following methods:-

  • Range
  • Quartile deviation
  • Mean deviation
  • Standard deviation

1.1       Range

It is define between the largest and smallest item in the given distribution. Then, it is defined by the following formula.

Range = L- S, where l = largest item and s = smallest item.

2.1.1 Calculation of Range in Science :-

Mark obtained by 30 students of Janasahayog Higher Secondary School in science of class – 9 are given below in ascending order. 7, 11, 15, 16, 17, 17, 25, 32, 32, 32, 32, 34, 34, 35, 35, 37, 39, 39, 41, 41, 43, 44, 45, 48, 52, 54, 56, 57, 58, 83

Here, R = L – S

= 83 – 7

= 76

Range of 30 students is 76. This type of statistics is called heterogeneous statistics and the range is known heterogeneous. Some students are getting low mark and some are getting high mark. It means there is gap on group.

Co-efficient of range = (L-S)/(L+S) =(83-7)/(83+7)=76/90

Co-efficient of range = 0.84

It shows very high variation in the subjects so group is heterogeneous. There is no constancy in obtain marks of Science

2.1.2 Calculating the Range in English

Mark obtained 30 student of class 9 in English is ascending order 14, 17, 19, 20, 23, 24, 24, 32, 32, 32, 32, 32, 32, 33, 33, 34, 34, 34, 36, 36, 40, 40, 42, 42, 44, 48, 48, 49, 67, 69

Co-efficient of range = (L-S)/(L+S) =(69-14)/(69+14) =55/83

Co-efficient of range = 0.66

Range is more than 0.5. so, group of distribution is heterogeneous. Achievement level of student shows variation in the subjects.

Table No. 11

Comparison between the Range of science and English.

Subject No. of Students Range Co-efficient of Range
Science 30 76 0.84
English 30 55 0.66

Both subject co-efficient ranges are above the value hence it is heterogeneous group of student in the distribution of science and English subject. So, co-efficient range is not significant and effective.

2.2 Standard Deviation

It is the measure of dispersion. It is defined as the positive square root of the arithmetic mean of the square deviation from their arithmetic mea of a set of value. It is also known as Root Mean, Square Deviation. It is very stable and reliable method of measures dispersion. It is calculated as below:

  1. i) Individual Series                                                                         ii) Discrete Series

 

Calculation

  • Mark obtain in Nepali subject by 30 students of class XI final examination 2071 at JanaShahayog Higher School arranged in ascending order given below: 21, 34, 35, 35, 35,36, 37, 37, 37, 40, 40, 41, 42, 42, 44, 44, 45, 45, 45, 47, 50, 51, 52, 55, 57, 62, 62, 62, 62, 69

Table No. 12

marks obtain Nepali subjects of class XI

Mark (x) Frequency (f) Mid-value (m) d= (m-a)/i fd fd2
20-30 1 25 -2 -2 4
30-40 10 35 -1 -10 10
40-50 10 45 0 0 0
50-60 4 55 + 1 4 4
60-70 5 65 + 2 5 2
N=30 Ed=0 Efd=-3 Efd2=38

It cannot be compare with other statistical data. so co-efficient of standard deviation should be calculated.

Now co-efficient of standard deviation

Co-efficient of standard deviation shows less than standard value so, it can be concluded the distribution is homogenous. 11.22 S.D. shows not so variance and distribution is not so scattered. Achievement level of the students is not so varies.

  • Marks obtain in English of class XI in ascending order : 04,04,04,05,07, 07,10, 13,14,20,21,21,24,26,27,35,35,35,35,37,40,40,41,44,48,49,51,51,60,62

Table No. 13

Marks obtain English subjects of class XI

Mark (x) Frequency (f) Mid-value (m) d=(m-a)/i fd fd2
0-10 6 5 -3 -18 54
10-20 3 15 -2 -6 12
20-30 6 25 -1 -6 6
30-40 5 35 0 0 0
40-50 6 45 + 1 +6 6
50-60 2 55 +2 +4 8
60-70 2 65 +3 +6 18
N=30 Efd=-14 Efd2 =104

   

Co-efficient of standard deviation shows less than standard value so, it can be concluded the distribution is homogenous. 18.03 S.D. shows not so variance and distribution is not so scattered. Achievement level of the students is not so varies

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