# find the 50th percentile, the 3rd percentile & the 33rd percentile to 1,2,4,7,8,9,10,20

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To find the percentile, you can follow this procedure. I will use the 33rd percentile as I show the steps.

1) Order all the data points from smallest to largest.

You did that.

2) Multiply 33% (0.33) by the total number of data points, n. If the result isn't a whole number, round it up to the next whole number. This is called the index.

0.33*8 = 2.64 --> 3

3) Count up that number of data points

Here, we count up 3 digits starting from the left. That is the number 4.

4) a) If you had to round, that value is the percentile

b) If you didn't have to round, the percentile is the average of that number and the next number following it.

Here, we had to round. Therefore, 4 would be the 33%-ile.

Following the same steps for the others:

3%-ile = 1. In short, we get 0.03*8 = 0.24 --> 1. So, we count up one number. So, we get 1.

50%-ile = 7.5. In short, we get 0.50*8 = 4. So, we count up four numbers, getting the number 7. We find the average of 7 and the next number, since we didn't have to round. So, (7+8)/2 = 7.5

Data = 1,2,4,7,8,9,10,20

50th percentile = ?

3rd percentile = ?

33rd percentile = ?

Formula for percentile: `P_(k)= {k(n+1)}/100 th`

k= 1,2,4...

n= number of data

**50th percentile**

`P_(50) = {50(8+1)}/100 th`

` `

= 4.5th value

Since 4.5th value is in between 4th and 5th value therefore,

`P_(50) = 7 + 0.5(8-7)`

`P_(50) = 7.5`

**3rd Percentile:**

`P_(3) = {3(8+1)}/100 th`

` `

= 0.27 th value

Since 0.27th value domes before 1 we will round off 0.27 which will become **1**.

**33rd percentile**

`P_(33) = {33(8+1)}/100 th`

` `** = **2.97 th value

2.97th value is the 3 rd value therefore 33rd percentile is **4**.

` `

A percentile is where all the values below a percentage of data falls. In order to find percentile you must first put your data in order, which is already done.

Next, you will multiply the percentile you want, I'll use 50, by how many numbers you have in your data set. .5*8=4 (no rounding is necessary because it is a whole number). After this you will count 4 numbers of your data set and whatever the fourth number is will be your 50th percentile. However, since there was no rounding in the step before, you must find the average of the fourth number and the number after (7 & 8). Your 50th percentile is **7.5**.

The same steps will be used for the other problems.

.03*8=.24 ----> round to 1. The first number will be your 3rd percentile, which is **1**.

.33*8= 2.64 ----> round up to 3. Count three numbers and your 33rd percentile is **4**.