Answer to Question #137996 in Statistics and Probability for Simone

Question

11. Following are the number of grams of carbohydrates in a 12 oz espresso beverage offered at Starbucks.

14 43 38 44 31 27 39 59 9 10 54

14 25 26 9 46 30 24 41 26 27 14

a) Find the first and third quartiles of these data. _____________, ______________

b) Find the median ___________________

c) Find the upper and lower boundaries: Upper _______________, Lower ______________

d) The beverage with the most carbohydrates is a Peppermint White Chocolate Mocha with 59 grams is this an outlier? _________________________

e) Construct a boxplot of the data.

f) Describe the shape of the distribution.

Answer 1

n = 22

Ordered from smallest to largest:

$9,9,10,14,14,14,24,25,26,26,27,$

$27,30,31,38,39,41,43,44,46,54,59$

Part a)

From excel, the data is contained in cells A1:A22.

The first quartile is obtained as

$=QUARTILE(A1:A22, 1)= 16.5$

The third quartile is obtained as

$=QUARTILE(A1:A22, 3)= 40.5$

answer: q1 = 16.5 and q3 = 40.5

part b)

the median is the 2nd quantile

$=QUARTILE(A1:A22, 2)=27$

answer: median = 27

Part c)

The inter quartile range is

$IQR = Q3-Q1= 40.5-16.5=24$

Upper boundary

$Q3 + 1.5* IQR$

$40.5 + 1.5*24=76.5$

Lower boundary

$Q1 - 1.5* IQR$

$16.5-1.5*24= -19.5$

Answer: the lower boundary is -19.5 and the upper boundary 76.5. But because weight cannot be a negative number, the lower boundary can be taken as

Part d)

The peppermint beverage is not an outlier since it is within the upper and lower boundaries

Part e)

Box plot

Part f)

The weights are negatively skewed since the median is closer to the upper quartile