Question

Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one producer to another. In May 2013, the author went to a certain website, randomly selected 10 zinfandels from among the 325 available, and obtained the following values of alcohol content (%).

14.9 14.5 16.2 14.3 15.9
13.7 16.2 14.6 13.9 15.1
A. Calculate the interpret several measures of center.
B. Calculate the sample variance using the defining formula.

Answer 1

Kindly check explanation

B) 0.829

Explanation:

Given the data :

% Alcohol content of 10 zindafel wine

14.9 14.5 16.2 14.3 15.9

13.7 16.2 14.6 13.9 15.1

Sorted value : 13.7, 13.9, 14.3, 14.5, 14.6, 14.9, 15.1, 15.9, 16.2, 16.2

Range = maximum - minimum

Range = 16.1 - 13.7

n = number of samples = 10

Median = 1/4(n + 1)th term

Median = 1/4(10+1)th term = 11/4 = 2.75 th term

(14.3 + 14.5) / 2 = 28.8 /2 = 14.40

Mode = 16. 2 ( most occurring observation)

Mean(m) = (13.7 + 13.9 + 14.3 + 14.5 + 14.6 + 14.9 + 15.1 + 15.9 + 16.2 + 16.2) / 10

= 149.3 / 10

= 14.93