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Measure of Central Tendency

  1. Measure of Central Tendency

It is one of the most important tools of statistical analysis to get one single value which describes the characteristics of entire mass of mun widely data. It is called central value or average or the expected value of the variables. We know the word ‘average’ is commonly used day to day conversation by everyone. So average is a single value which represents the group of value that has great significance.

Measure of central tendency shows the tendency of some central value around which data tends to cluster around of single value which represented to the whole distribution. To measure central tendency methods are given below.

  1. Mean
  2. Median
  3. Mode

Beside these there is less important average like moving average, progressive average but these are no so popular in application level. Hence we do not use ‘mode’ also.

1.1       Mean

It is the most popular method used in central tendency. It is mostly called average or arithmetic mean. It is represented by X mean can be calculated by the following methods.

  • Continuous series

 

 

  1. Individual series:

Individual data is collected from Shree JanaSahayog higher secondary school, Hansposha (class XI) Nepali.

Mark obtained in Nepali – 35, 35, 51, 45, 47, 45, 62, 69, 62, 37,45, 40, 34, 62, 40, 42, 62, 35, 57, 41, 55, 42, 37, 50, 37, 21, 44, 36, 52, 44,

Mean

= 1364/30

= 45.47

From the above mean value 45.47 indicates that the students of Janasahayog Higher Secondary of grade XI achieved level in nepali cubject is normal standard. Where 17 (56.67%) lies below the mean value and 13 (43.35%) lies above mean value.

Marks obtain in English of class XI for calculating Mean of janasahayog Higher Secondary of  itahari -24

21,21,35,26,35,49,51,35,51,41,20,13,62,44,35,37,60,27,40,5,24,40,4,48,17,7,10,14,4,4

=880/30

=29.33

from the above mean value 29.33 indicates  that the students of janashayoug higher secondary school class XI in students achievement  level in English is not satisfaction .the marks of students is poor in English so we can say it is not consistency also .

 

Table – 1

comparing Nepali and English in class XI

Subject No of student Below average  % Mean value Above average
Nepali 30 56.67% 45.47 43.33%
English 30 46.66% 29.33 53.33%

 

In the above data shows the mean value of Nepali is better than English. So English subject mark is very low in comparison with Nepali subject.

Similarly the mark obtained by class 9 in science and English are compared below (Data Collect) from Janasahayog H.S.S. Itahari – 24, Tarahara.

  • Mark obtained in science is in ascending order : 7, 11, 15, 16, 17, 17, 23, 32, 32,32,32, 34, 34, 35, 35, 37, 39, 39, 41, 41, 43, 44, 45, 48,52, 54, 56, 57, 58, 83.
  • Table No – 2

The mark obtained by class 9 in science

Mark No of students(f) Mid value fx
5 – 15 2 10 20
15 – 25 5 20 100
25 – 35 6 30 180
35 – 45 9 40 360
45 – 55 4 50 200
55 – 65 3 60 180
65 – 75 0 70 0
75 – 85 1 80 80
  N = 30    = 1120

Here mean ( ) =

= 1120/30 = 37.33

Mean value is 37.33 which indicates the achievement level of student is normal but not so satisfactory in science subject. Here 14(46.67%) students are lies below the average marks and 16(53.33%) students’ lies above the average marks. However the pass percentage is batter because out of 30 students and 23 students has pass.

Calculation of mean

  • Mark obtained in English of class IX is in 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.

Table No – 3

Mark obtained in English

Mark No of students (f) Mid value fx
10 – 20 3 15 45
20 – 30 4 25 100
30 – 40 13 35 455
40 – 50 8 45 340
50 – 60 0 55 0
60 – 70 2 65 130
  N = 30    = 1070

Here mean ( ) =

= 1070/30

= 35.67

The mean value of 30 students in English is 35.67. It is the not good achievement of student of class 9 of Janasahayog  higher secondary school  Itahari – 24, Tarahara and it indicates that the mean is normal because 20(66.67%) lies below average mark and 10(33.33%) lies above average mark. However the percentage level is better.

Table No – 5

Comparison mark between English and Science of class IX

Subject Mean value No of student Below average % Above average %
English 35.67 30 66.67% 33.33%
Science 37.33 30 46.67% 53.33%

 

From the above table the two subject mean value is neither nearly same nor so different (35.55/37.33) English and science. But the result is better not so bad because only seven students are failed in exam result 23/23 students were passed and the pass percentage is satisfactory.

1.2       Median

The median is the exact midpoint of the series, below and above which 50 % of the cases lie. It divides the total number of observation into two equal groups and it is also called the positional average. Median is denoted by md and it is calculate as following methods:

Calculation

  1. Mark obtained by 30 students of shree janasahayog higher secondary school Hansposa final examination 2071 (class XI subject English)

Ascending order: 04, 04, 04, 5, 7, 7, 10, 13, 14, 20, 21, 21, 24, 26, 27, 35, 35, 35, 35, 37, 40, 40, 41, 44, 48, 49, 51, 51, 60, 62.

  1. Individual series

 item

=  = 15.5th item = 35 item

Therefore, md = 35

  1. Discrete series

= 31/ 2 = 15.5

Md = 35

The median value is 35 and it is not satisfactory and constancy .However the past percentage is batter because 50% students have passed the exam. Here 15(50%) and below the average marks 4(13.33%) students are lies equal of median and 11(36.67%) students’ lies above the average marks.

  • Mark obtains in Nepali XI is put in ascending order: 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 – 6

Marks obtain in Nepali class XI in median

Mark No of student cf
20 – 30 1 1
30 – 40 8 9
40 – 50 11 20
50 – 60 5 25
60 – 70 5 30
  N = 30  

 

Here, N/2  = 30/2 = 15th item and it lies  of (40 – 50) item

Where, f = 11, cf = 9,  n/2=15, i= 10, L = 40

= 40 + (15-9)/11  x 10

=40+(6/11)x10

= 40+5.45

=45.5

The median value 45.45 indicates low achievement level of students in Nepali and it is not also satisfactory where 19(63.33%) student lies below median value and rest of 11(36.67%) lies above the median value.

  • Comparison mark between English and Science of class IX

Table No – 7

Comparison mark between English and Nepali of class XI

Subject Median value No of student Below average % Equal Above average %
English 35 30 50 13.33 36.67
Nepali 45.45 30 63.63 36.67

 

From the above table the two subject median is different in Nepali level of     value is neither nearly same nor so different (35/45.45) English and Nepali.

  • Calculation of median in science, mark obtained by 30 students of Janasahyog higher secondary school Itahari – 24, Tarahara class – IX final examination 2071.

Table No – 3

Mark obtained Frequency (f) cf
0-10 1 1
10-20 5 6
20-30 1 7
30-40 11 18
40-50 6 24
50-60 5 29
60-70 0 29
70-80 0 29
80-90 1 30
                                                                                              Total =3o

=  = (31/2)th item = 15.5 item (lies in 30-40 cf)

n/2=15.5                  L=30                               F=11

CF=7               i=10

=30+(15-7) x 10/11

=30+7.27

=37.27

The above median value 37.27 is not so satisfactory achievement in science of class 9 Janasahayog higher school  out of 30 students 16(53.33%) have got  marks below  median value and 14(46.67%) have above the median value .

 

  • Calculation of median in English of class IX of janasahayog Itahari – 24 marks obtained in 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.

Table No – 9

marks obtain in median in English of class IX

Mark obtained No of Students Cf
10-20 3 3
20-30 4 7
30-40 13 20
40-50 8 28
50-60 0 28
60-70 2 30
F = 30

Here, Md = 

size of  item =   = 15.5 it lies (30-40)

F=13            cf=7                             l=30

i=10

= 30+(15-7)x10 /11

= 30+ 80/11

=30+6.15

= 36.15

Above median value shows Md value of English of class IX is 36.15 it is not good achievement however the pass percentages is batter out of 30 students only 7 have failed and 23 have passed .   Better result in English subject where 20(67.67%) have got student lies below median value and rest of 10(33.33%) student lies above the median value. As a result according to the percent is satisfactory.

Table No – 10

Comparison between two median class IX students in science and English

Subject Median value Total no of students Below md value Above value
English 36.15 30 20 10
Science 37.27 30 16 14

The result between two subject is not so different and pass percentage is also satisfactory.

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