Answer to Question #338680 in Statistics and Probability for shimmy

Question

The scores of Miss San Quintin candidates from seven judges were recorded as follows: 8.12, 9.10, 8.42, 9.14, 8.75, 9.17, and 8. 37 

For numbers 4 – 6, refer to the given data above.

4. Find the 50th percentile or P50 of the judges’ scores.

5. What is the P30 of the judges’ scores? 

6. Determine the 70th percentile of the judges’ scores

7. Calculate P40 of the judges’ scores

Answer 1

4. To get the percentile in a given set of data, the data should be sorted from lowest to highest. 

$$8.12, 8. 37, 8.42, 8.75, 9.10, 9.14, 9.17$$

$P50=\dfrac{50}{100}(7+1)=4$

It means that the P50 is the 4th rank of the sorted data set.

The 4th rank of the sorted data set is 8.75.

 A 50th percentile is the same as a "median." 

$$median=8.75$$

8.75

5. To get the percentile in a given set of data, the data should be sorted from lowest to highest. 

$$8.12, 8. 37, 8.42, 8.75, 9.10, 9.14, 9.17$$

$$n=7$$

$P30=\dfrac{30}{100}(7+1)=2.4$

We rounded down P30 to 2 and what it means is that the P30 is the 2nd rank of the sorted data set.

The 2nd rank of the sorted data set is 8.37

8.37

6. To get the percentile in a given set of data, the data should be sorted from lowest to highest. 

$$8.12, 8. 37, 8.42, 8.75, 9.10, 9.14, 9.17$$

$$n=7$$

$P70=\dfrac{70}{100}(7+1)=5.6$

We rounded down P70 to 6 and what it means is that the P70 is the 6th rank of the sorted data set.

The 6th rank of the sorted data set is 9.14

9.14 

7. To get the percentile in a given set of data, the data should be sorted from lowest to highest. 

$$8.12, 8. 37, 8.42, 8.75, 9.10, 9.14, 9.17$$

$$n=7$$

$P40=\dfrac{40}{100}(7+1)=3.2$

We rounded down P40 to 3 and what it means is that the P40 is the 3rd rank of the sorted data set.

The 3rd rank of the sorted data set is 8.42

8.42