Question

Following are the number of grams of carbohydrates in a sample of 12-ounce espresso beverages offered at Starbucks. 6 , 9, 10, 20, 22, 25, 27, 40 , 48, 59 What percentile is the beverage that has 40 grams of carbohydrates in it? Write only a number as your answer (for example, for the 23rd percentile, write 23).

Answer 1

Answer:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1,  2 , 3,  4,    5,   6,    7,   8,    9,    10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

$p=\frac{8}{10} *100 = 80$

So the  the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.

Step-by-step explanation:

We can define a percentile as "a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it"

For this case we have the following data given:

6 , 9, 10, 20, 22, 25, 27, 40 , 48, 59

And we want to calculate the percentile for the value of 40 grams

Since the dataset is on increasing way there is no problem to calculate this percentile.

We see that we have a total of n =10 observations, and we can rank the position of each observation (i) like this:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1,  2 , 3,  4,    5,   6,    7,   8,    9,    10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

$p=\frac{8}{10} *100 = 80$

So the  the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.