Sagot :
Answer:
Percentiles are a measure of the relative standing of observation within a data. Percentiles divide a set of observations into 100 equal parts, and percentile scores are frequently used to report results from national standardized tests such as NAT, GAT, etc.
The pth percentile is the value Y(p) in order statistic such that p percent of the values are less than the value Y(p) and (100-p) percent of the values are greater Y(p) . The 5th percentile is denoted by P5, the 10th by P10 and 95th by P95.
Percentiles for the ungrouped data
To calculate percentiles (a measure of the relative standing of an observation) for the ungrouped data, adopt the following procedure
Order the observation
For the mth percentile, determine the product m.n100. If m.n100 is not an integer, round it up and find the corresponding ordered value and if m.n100 is an integer, say k, then calculate the mean of the Kth and (k+1)th ordered observations.
Example: For the following height data collected from students find the 10th and 95th percentiles. 91, 89, 88, 87, 89, 91, 87, 92, 90, 98, 95, 97, 96, 100, 101, 96, 98, 99, 98, 100, 102, 99, 101, 105, 103, 107, 105, 106, 107, 112.
Solution: The ordered observations of the data are 87, 87, 88, 89, 89, 90, 91, 91, 92, 95, 96, 96, 97, 98, 98, 98, 99, 99, 100, 100, 101, 101, 102, 103, 105, 105, 106, 107, 107, 112.
P10=10×30100=3
So the 10th percentile i.e P10 is 3rd observation in sorted data is 88, means that 10 percent of the observations in data set are less than 88.
P95=95×30100=28.5
29th observation is our 95th percentile i.e. P95=107.
Percentiles for the Grouped data
The mth percentile (a measure of the relative standing of an observation) for grouped data is
Pm=l+hf(m.n100−c)
Like median, m.n100 is used to locate the mth percentile group.
l is the lower class boundary of the class containing the mth percentile
h is the width of the class containing Pm
f is the frequency of the class containing
n is the total number of frequencies Pm
c is the cumulative frequency of the class immediately preceding to the class containing Pm
Note that 50th percentile is the median by definition as half of the values in the data are smaller than the median and half of the values are larger than the median. Similarly, 25th and 75th percentiles are the lower (Q1) and upper quartiles (Q3) respectively. The quartiles, deciles, and percentiles are also called quantiles or fractiles.
Deciles, Percentiles for Grouped data
Measure of relative standing of an observation in Grouped Data
Example: For the following grouped data compute P10 , P25 , P50 , and P95 given below.Solution:
Locate the 10th percentile (lower deciles i.e. D1)by 10×n100=10×3o100=3 observation.
so, P10 group is 85.5–90.5 containing the 3rd observation
P10=l+hf(10n100−c)=85.5+56(3−0)=85.5+2.5=88
Locate the 25th percentile (lower quartiles i.e. Q1) by 10×n100=25×3o100=7.5 observation.
so, P25 group is 90.5–95.5 containing the 7.5th observation
P25=l+hf(25n100−c)=90.5+54(7.5−6)=90.5+1.875=92.375
Locate the 50th percentile (Median i.e. 2nd quartiles, 5th deciles) by 50×n100=50×3o100=15 observation.
so, P50 group is 95.5–100.5 containing the 15th observation
P50=l+hf(50n100−c)=95.5+510(15−10)=95.5+2.5=98
Locate the 95th percentile by 95×n100=95×3o100=28.5th observation.
so, P95 group is 105.5–110.5 containing the 3rd observation
P95=l+hf(95n100−c)=105.5+53(28.5−26)=105.5+4.1667=109.6667
The percentiles and quartiles may be read directly from the graphs of cumulative frequency function.
Step-by-step explanation:
Percentiles are the values of arranged data which divide whole data into hundred equal parts. They are 9 in numbers namely P1,P2,⋯,P99 . Here P1 is first percentile, P2 is second percentile, P3 is third percentile and so on.Percentiles for the Grouped data
Locate the 10th percentile (lower deciles i.e. D1)by 10×n100=10×3o100=3 observation. ...
Locate the 25th percentile (lower quartiles i.e. Q1) by 10×n100=25×3o100=7.5 observation. ...
Locate the 50th percentile (Median i.e. 2nd quartiles, 5th deciles) by 50×n100=50×3o100=15 observation.
The variance of a population for ungrouped data is defined by the following formula: σ2 = ∑ (x − x̅)2 / n.Percentiles are the values of arranged data which divide whole data into hundred equal parts. They are 9 in numbers namely P1,P2,⋯,P99 . Here P1 is first percentile, P2 is second percentile, P3 is third percentile and so on.
Answer:
To find that, you should Arrange the data in ascending order like:
9, 10, 12, 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 21, 22, 25, 27, 29, 30
Step-by-step explanation:
Hope it helps;)