## Percentiles in R

So much time people need to calculate percentiles in statistics. This is a little as R failed to have no inbuilt function for that like quantiles and mean.

So how do we go about this?? Well some people accept the we should use the general formula

P(N+1)/100. Where p is the percentile value. They believe this will actually tell us the position of such percentiles.

However, this isn't always true infact most of the time it's not accurate.

#### What is the best way to find percentile??

Well, there is inbuilt function in R to do that but only few people aware of that.

What! There's inbuilt function for??

Don't doubt it, it's even what you know.

To calculate your percentiles use `quartile()`

function. inside it includes parameters called 'prob' and equal to your percentiles.

Our formula structure look like this

`quantile(data, percentage)`

Let's take a look at some

#### Example1.

Let say I need to find the 20 percentiles of the following data.

1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7.

```
data=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
quantile(data,0.2)
```

Results

```
data=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
> quantile(data,0.2)
20%
3
```

Note: we are to change the percentage value to decimal, 20% =0.2. that is why we type 0.2.

Now let's try another example

#### Example 2

find height of the 40 percentiles of the following heights.

11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17

**Codes>>**

```
allHeight=c(11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17)
percent40=quantile(allHeight,0.4)
print(percent40)
```

Result>>

```
> percent40=quantile(allHeight,0.4)
> print(percent40)
40%
17
```

can you see how easy it is to find your percentiles?? if you are given the following percentiles you type their respective value.

percentiles | percent/100 | value to be typed |
---|---|---|

3% | 3/100 | 0.03 |

15% | 15/100 | 0.15 |

55% | 55/100 | 0.55 |

So always remember to convert your percentage to decimal.

#### How to calculate the Quartiles

To calculate quartile is a little thing in R. just used the quantile() function.

#### Example

calculate the first quantile of the following heights.

11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17.

SOLUTION

Codes>>

```
height=c(11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17)
print(quantile(height))
```

Results>>

```
> height=c(11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17)
> print(quantile(height))
0% 25% 50% 75% 100%
11.0 17.0 18.5 25.0 36.0
```

Note: the first quantile is below 25%, second quantile below 50%, third quantile is below 75%. etc.

#### What if you need to find your quantiles without listing unnecessary one??

I still get your back on that too but note the following fact.

Quantile | Percentile |
---|---|

first quantile | 25% |

second quantile | 50/100 |

third quantile | 75/100 |

The table above is show the equality between quantile and percentile. Therefore to find the first quantile in the previous question, we find the 25th percentile. so our codes look like the following

codes

```
height=c(11,22,17,13,27,25,17,27,23,17,19,22,17,19,16,23,25,17,36,15,14,25,26,17,18,29,17,15,28,17)
firstQuatile=quantile(height,0.25)
print(firstQuantile)
```

Result>>

```
> firstQuatile=quantile(height,0.25)
> print(firstQuantile)
Error in print(firstQuantile) : object 'firstQuantile' not found
> print(firstQuatile)
25%
17
```

### Example2

calculate the third quantile from the following data.

1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7.

### Solution

Firstly note that third quantile is equivalent to 75%. therefore we use 75% which is going to be change to 0.75.

Codes>>>

```
mydata=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
thirdQuatile=quantile(height,0.25)
print(thirdQuantile)
```

Result>>

```
> mydata=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
> thirdQuantile=quantile(height,0.25)
> print(thirdQuantile)
25%
17
```

Can you see how easy it is??.

#### How to calculate Deciles in R.

well, we don't have any inbuilt function for decile too, However we can also use equaivalent percentile. how do we do that??? keep calm it is as easy as 1+1.

To Calculate Decile use quantile() function also. and input the conversion of your decile(in decimal ) inside the parameters.

For example.

first-Decile == 1/10 =0.1

second-Decile == 2/10 = 0.2

Third-Decile== 3/10 = 0.3.

you can continue the logic like that to finish all.

#### How to write code to calculate Deciles

without wasting time, let's take a look at some question on this Decile.

#### Example1.

calculate the third-decile of the following data.

1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7.

Solution

we know that third decile is same as 3/10 i.e 0.3. therefore our codes will be the following

```
data=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
thirdDecile=quantile(data,0.3)
print(thirdDecile)
```

**Result**

```
>data=c(1,2,1,3,7,5,7,7,3,7,9,2,7,9,6,3,5,7,6,5,4,5,6,7,8,9,7,5,8,7)
> thirdDecile=quantile(data,0.3)
> print(thirdDecile)
30%
5
```

Now try to find the sixth,seventh,eighth and nineth decile.

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