Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

THE DATA BELOW REPRESENT THE AMOUNT OF GRAMS OF CARBOHYDRATES IN A SERVING OF BR

ID: 3157588 • Letter: T

Question

THE DATA BELOW REPRESENT THE AMOUNT OF GRAMS OF CARBOHYDRATES IN A SERVING OF BREAKFAST CEREAL

10 15 23 29 19 23 21 20 15 25 18

SHOW FORMULA AND CALCULATIONS

THE MEAN CARBOHYDRATES IN THIS SAMPLE IS ____ GRAMS

THE MEDIAN CARBOHYDRATES AMOUNT IN THE CEREAL IS ____ GRAMS

THE FIRST QUARTILE OF THE CARBOHYDRATE AMOUNTS IS _____ GRAMS

THE THIRD QUARTILE OF THE CARBOHYDRATE AMOUNTS IS______ GRMAS

THE RANGE IN THE CARBOHYDRATE AMOUNTS IS _______ GRAMS

THE INTERQUARTILE RANGE IN THE CARBOHYDRATE AMOUNTS IS ______ GRAMS

THE VARIANCE OF THE CARBOHYDRATE AMOUNTS IS________

THE STANNDARD DEVIATION OF THE CARBOHYDRATE AMOUNTS IS ____________ GRAMS

THE COEFFICIENT OF VARIATION OF THE CARBOHYDRATE AMOUNTS IS ______%.

Explanation / Answer

Ordering the data,

10
15
15
18
19

20

21
23
23
25
29

*************************************

a)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    218      
As n =    11      
Thus,          
X =    19.81818182   [ANSWER, MEAN]

*****************************************
b)

Th median is the middle (6th value),

Median = 20 [ANSWER]

***************************************

c)

The first quartile is the median of the lower half,

Q1 = 15 [ANSWER]

***************************************
d)

The third quartile is the median of the upper half,

Q3 = 23 [ANSWER]
  
***************************************
e)
          
Also, we have          
          
Maximum =    29      
Minimum =    10      
Range = max - min =    19      

******************************  

F)

Hence,

IQR = Q3 - Q1 = 8 [ANSWER]

********************************

g)
      
Setting up tables,          


Thus, Sum(x - X)^2 =    279.6363636      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    11      
          
s^2 =    27.96363636 [ANSWER, VARIANCE]

******************************************

g)


Thus,          
          
s =    5.288065465 [ANSWER, STANDARD DEVIATION]

***************************************

h)

coefficient of variation = s/X = 5.288065465/19.8181818181*100% =   26.6828991% [ANSWER]

************************************

Hi! There are other methods in determining the quartiles. If you have another method in your class, please resubmit this question indicating what method you use in your class. That way we can continue helping you! Thanks!

x x - X (x - X)^2 10 -9.81818 96.39669 15 -4.81818 23.21488 15 -4.81818 23.21488 18 -1.81818 3.305785 19 -0.81818 0.669421 20 0.181818 0.033058 21 1.181818 1.396694 23 3.181818 10.12397 23 3.181818 10.12397 25 5.181818 26.85124 29 9.181818 84.30579