Question

Caffeine: Following are the number of grams of carbohydrates in 12-ounce espresso beverages offered at a coffee shop. 44 29 11 61 15 38 20 41 42 25 26 10 30 12 18 40 21 24 43 6 46 55 34 35 Send data to Excel Part: 0 / 40 of 4 Parts Complete Part 1 of 4 Your Answer is incorrect (a) Find the first and third quartiles of these data. The first quartile of these data is . The third quartile of these data is

Answer 1

`Q_1 = 19` --- first quartile

`Q_3 = 41.5` --- third quartile

Explanation:

Required:

The first and the third quartile

First, we order the dataset in ascending order
`Sorted: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29, 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61`

The count of the dataset is:

`n = 24`

Calculate the median position

`Median=(n+1)/(2)`

`Median=(24+1)/(2)`

`Median=(25)/(2)`

`Median=12.5th`

This means that the median is between the 12th and the 13th item

Next;

Split the dataset to two parts: 1 to 12 and 13 to 24

`First: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29`

`Second: 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61`

The median position is:

`Median = (n + 1)/(2)`

In this case; n = 12

So:

`Median = (12 + 1)/(2)`

`Median = (13)/(2)`

`Median = 6.5th`

This means that the median is the average of the 6th and 7th item of the sorted dataset

So, we have:

`Q_1 = (18 + 20)/(2)`

`Q_1 = (38)/(2)`

`Q_1 = 19` --- first quartile

`Q_3 = (41+42)/(2)`

`Q_3 = (83)/(2)`

`Q_3 = 41.5` --- third quartile