# While calculating percentile rank there are two formula 1st ) percentile ={ ( number of values below x + 0.5)/total number of observation } *100 2nd ) percentile ={ ( number of values below x )/total number of observation } *100 I have to know when to used 1st formula and when to used 2nd formula propert explanation needed

While calculating percentile rank there are two formula
1st )
percentile ={ ( number of values below x + 0.5)/total number of observation } *100
2nd )
percentile ={ ( number of values below x )/total number of observation } *100
I have to know when to used 1st formula and when to used 2nd formula
propert explanation needed
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Hayden Espinoza
The percentiles represent the percentage of data which is less than equal to given particular value. For example 30th percentile value is nothing but the value below which 30% of data values are observed.
The percentiles divide the data distribution into 100 equal parts, which is used to interpret on standardized data distribution. Percentile rank is nothing but the percentage of scores which are lower than or equal to that particular score in a frequency distribution.
Percentage rank is between 1 and 99 and for example percentile rank of a student in test score is 90 is nothing but that particular student scored better than 90% of students.
There are two formulas which we use to calculate the percentage ranks

Here M is number of ranks below X
R is number of ranks equals to X
Y is total number of ranks
This formula is used when we need to calculate the percentile rank of a particular score x, where x is included.
For example there are 30 students in a class where two students Robert and Smith got same rank 15th. The percentile rank of Robert is calculated as shown below
The total number of ranks are nothing but total number of students Y=30
The total number of ranks less than 15th rank are M=14
The total number of ranks equal to 15th rank(Since two students got same rank) R=2
The percentile rank of Robert $=\left(\frac{M+0.5×R}{Y}\right)×100=\left(\frac{14+0.5×2}{30}\right)×100=50\mathrm{%}$
The second formula for percentile rank is
$\text{Percentile rank}=\left(\frac{M}{Y}\right)×100$
M is the number of ranks below X
Y the total number of ranks.
For example the scores of 10 students in tests are shown below
55 60 65 68 70 75 80 85 88 92
To calculate the percentile rank of score 80. Since there are no multiple students with same score 80, we use the second formula. Each score is assigned a rank from 1 to 10 with respect to order.
The number of ranks below score 80 M=6
Total number of ranks Y=10
The percentile rank of score 80 $\text{Percentile rank}=\left(\frac{M}{Y}\right)×100=\frac{6}{10}×100=60\mathrm{%}$