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

Answer:

$Q_1 = 19$ --- first quartile

$Q_3 = 41.5$ --- third quartile

Step-by-step 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

$Median=\frac{n+1}{2}$

$Median=\frac{24+1}{2}$

$Median=\frac{25}{2}$

$Median=12.5th$

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:

$Median = \frac{n + 1}{2}$

In this case; n = 12

So:

$Median = \frac{12 + 1}{2}$

$Median = \frac{13}{2}$

$Median = 6.5th$

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

So, we have:

$Q_1 = \frac{18 + 20}{2}$

$Q_1 = \frac{38}{2}$

$Q_1 = 19$ --- first quartile

$Q_3 = \frac{41+42}{2}$

$Q_3 = \frac{83}{2}$

$Q_3 = 41.5$ --- third quartile