Question

According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. Wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. Random ratings of a pinot noir recently produced by a newly established vineyard in follow:
87 91 86 82 72 91
60 77 80 79 83 96

Required:
a. Develop a point estimate of mean wine score for this pinot noir (to decimals).
b. Develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals).

Answer 1

Answer:

a

$\= x = 82$

b

$s = 9.64$

Step-by-step explanation:

From the question we are told that

    The data is  87  91  86  82  72  91   60  77  80  79  83  96

Generally the point estimate for the mean is mathematically represented as

    $\= x = \frac{\sum x_i }{n}$

=>  $\= x = \frac{87 +91 + 86 + \cdots + 96}{12}$

=>    $\= x = 82$

Generally the point estimate for the standard deviation  is mathematically represented as

      $s = \sqrt{\frac{ \sum ( x_i - \= x )^2 }{ n -1 } }$

=>     $s = \sqrt{\frac{ ( 87 - 82 )^2 +( 91 - 82 )^2 + \cdots + ( 96 - 82 )^2 }{ 12 -1 } }$

=>     $s = 9.64$