Measurement of Relative Position application of statistics in educational research

**Measurement of Relative Position**

Relative position provides individual achievement of the students in comparision to each an every students. There for it is very stable procedure in evaluation of student in educational sector. Measure of central tendency shows average and state of distribution of given data in statistics which does not exist personal improvement in comparision to other students. Therefor relative measurement is more important process to evaluate individual progress in education field. It can be calculation as below:

- Percentile Rank 2. Quartile Rank

**4.1 Percentile Rank**

The percentile rank is the point in the distribution below which gives percentage of scorer fall or the term percentile rank may be define as the number representing the percentage of the total number of cases lying below the given score the value of percentile rank is between 0-100^{o}. If the no of student is more it can be calculated as making frequency table cumulative frequency and the obtained mark be calculated to find percentile rank as given formula.

Percentile Rank = PR = 100/N (cf -f/2 ) (Discrete Series)

Where, PR = Percentile Rank

cf = cumulative frequency

x = the some we want it PR.

I = size of class interval

l = lower limit

f = frequency of interval containing x.

N = Total number score

R = Series number

Table No. 18

Percentile rank of class IX students of science

Mark Obtain (x) | Frequency (f) | Cumulative Frequency (CF) | Percentile Rank (PR) | Position |

83 | 1 | 30 | 98.33 | 1^{st} |

28 | 1 | 29 | 95 | 2^{nd} |

57 | 1 | 28 | 91.67 | 3^{rd} |

56 | 1 | 27 | 88.25 | 4^{th} |

54 | 1 | 26 | 84.91 | 5^{th} |

52 | 1 | 25 | 81.58 | 6^{th} |

48 | 1 | 24 | 78.25 | 7^{th} |

45 | 1 | 23 | 74.92 | 8^{th} |

44 | 1 | 22 | 71.67 | 9^{th} |

43 | 1 | 21 | 68.33 | 10^{th} |

41 | 2 | 20 | 36.33 | 11^{th} |

39 | 2 | 18 | 56.67 | 12^{th} |

37 | 1 | 16 | 51.67 | 13^{th} |

35 | 2 | 15 | 41.67 | 14^{th} |

34 | 2 | 13 | 40 | 15^{th} |

32 | 4 | 11 | 30 | 16^{th} |

23 | 1 | 7 | 21.67 | 17^{th} |

17 | 2 | 6 | 16.67 | 18^{th} |

16 | 1 | 4 | 11.67 | 19^{th} |

15 | 1 | 3 | 8.33 | 20^{th} |

11 | 1 | 2 | 5 | 21^{th} |

7 | 1 | 1 | 1.67 | 22^{th} |

By analyzing the above table highest percentile rank of science subject of class – 9 is 98.33 and it obtain mark is 83 of Anish Basnet. In this way the lowest percentile rank is 1.67 and its obtain mark is 7 by Prabin Rai. Percentile rank is useful in calculation of position in evaluation so it is significant in evaluation.

**Mark obtain in English subject in Janasahayog H.H.S of class – 9 is going to be presented in percentile rank**.

Table No. 19

Percentile rank of class IX students of English

Mark (x) | Frequency (f) | cf | PR | Position |

69 | 1 | 30 | 98.33 | 1^{st} |

67 | 1 | 29 | 95 | 2^{nd} |

49 | 1 | 28 | 91.67 | 3^{rd} |

48 | 2 | 27 | 86.67 | 4^{th} |

44 | 1 | 25 | 81.67 | 5^{th} |

42 | 2 | 24 | 76.67 | 6^{th} |

40 | 2 | 22 | 70 | 7^{th} |

36 | 2 | 20 | 63.33 | 8^{th} |

34 | 3 | 18 | 55 | 9^{th} |

33 | 2 | 15 | 46.67 | 10^{th} |

32 | 6 | 13 | 33.33 | 11^{th} |

24 | 2 | 7 | 20 | 12^{th} |

23 | 1 | 5 | 15 | 13^{th} |

20 | 1 | 4 | 11.67 | 14^{th} |

19 | 1 | 3 | 8.33 | 15^{th} |

17 | 1 | 2 | 5 | 16^{th} |

14 | 1 | 1 | 1.67 | 17^{th} |

By analyzing above table the highest percentile rank of English is 98.33 by Ajita Basnet of class-9 and mark obtain is 69. In this way the lowest percentile rank is 1.67 and it’s obtain mark is 14 by Kiran Shrestha of class – 9.

By comparing the mark of two subject of class – 9 the highest percentile of value of both students is equal 98.33 although their obtaining mark are different 83 and 69. Such as the lowest percentile rank also 1.67 but the obtaining mark is different as 7 and 14.

**4.3 Quartile Rank**

It divides the statistical data into 4 equal parts. It is not more important as percentile because it provides value is not so reliability as percentile value. Quartile Rank is calculated as below:

QR = (CF. f/2)/N x 4

**Calculation**

Percentile rank of class IX students in science is calculated under the following. (Source : Shree Janasahayog H.S.S. Itahari-24.)

**Mark obtains in Nepali subject in Janasahayog H.S.S. of class – XI is going to be presented in quartile rank.**

Table No. 20

Mark obtains in Nepali subject

Mark (x) | Frequency (f) | cf | QR |

69 | 1 | 33 | 3.93 |

62 | 3 | 29 | 3.67 |

57 | 1 | 26 | 3.40 |

55 | 1 | 25 | 3.27 |

52 | 1 | 24 | 3.13 |

51 | 1 | 23 | 3 |

50 | 1 | 22 | 2.87 |

47 | 1 | 21 | 2.73 |

45 | 3 | 20 | 2.47 |

44 | 2 | 17 | 2.13 |

42 | 2 | 15 | 1.87 |

41 | 1 | 13 | 1.67 |

40 | 2 | 12 | 1.47 |

37 | 3 | 10 | 1.13 |

36 | 1 | 7 | 0.87 |

35 | 3 | 6 | 0.60 |

34 | 2 | 3 | 0.27 |

21 | 1 | 1 | 0.07 |

The above table shows 3.95 is the highest Q.R. value and 0.07 is the lowest value of Q.R. This quartile value is decreasing from top to bottom serially the highest mark 69 is by Anita Adhikari and the lowest mark 21 is by Bhima Magar.

**Mark obtain in English subject in Janasahayog H.S.S. of class – XI is going to be presented in quartile rank.**

Table No. 21

Mark obtain in English subject of class- XI

Mark (x) | Frequency (f) | cf | QR |

62 | 1 | 30 | 3.93 |

51 | 1 | 29 | 3.80 |

49 | 1 | 28 | 3.67 |

48 | 1 | 27 | 3.53 |

45 | 1 | 26 | 3.40 |

44 | 1 | 25 | 3.27 |

41 | 1 | 24 | 3.13 |

40 | 2 | 23 | 2.93 |

37 | 1 | 21 | 2.73 |

35 | 4 | 20 | 2.4 |

27 | 1 | 16 | 2.07 |

26 | 1 | 15 | 1.93 |

24 | 1 | 14 | 1.80 |

21 | 2 | 13 | 1.60 |

20 | 1 | 11 | 1.40 |

14 | 1 | 10 | 1.27 |

13 | 1 | 9 | 1.13 |

10 | 1 | 8 | 1 |

7 | 2 | 7 | 0.80 |

6 | 1 | 5 | 0.60 |

5 | 1 | 4 | 0.47 |

4 | 3 | 3 | 0.20 |

The above table shows 3.93 is the highest quartile rank and 0.20 is the lowest quartile rank value. This quartile rank value are decreasing from top to bottom serially. The highest mark 62 by Anuj Dahal and lowest mark is 04 by Barsha Khatri.

By comparing the mark of two subject of class XI English and Nepali the highest quartile rank value of both students is 3.93 but their obtaining mark are different 62 and 69. By Anuj Dahal and Anita Adhikari but the lowest quartile value are different 0.20 and 0.07. Thus, their obtaining mark also different 04 and 21 by Barsha Khatri and Bhima Magar.