In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows: Company A: 9.3 8.8 6.8 8.7 8.5
6.7 8.0 6.5 9.2 7.0
Company B: 11.0 9.8 9.9 10.2 10.1
9.7 11.0 11.1 10.2 9.6
(a) Calculate the sample mean and median for the data for the two companies.
(b) Plot the data for the two companies on the same line and give your impression regarding any apparent differences between the two companies.

(a) Company A sample mean = 7.9; Company B sample mean = 10.26; Company A median = 8.25; Company B median = 10.15

(b) See the attached pdf file for the line plot. In the graph, Company A data is plotted using small circle dots while Company B data is plotted using small cross dots.

From the graph, apparent differences between the two companies is that the rods steel of B appear to be more flexible than the rod steel of company A.

Step-by-step explanation:

(a) Calculate the sample mean and median for the data for the two companies.

(i) Sample mean

A sample mean can be described as the average of a data set. The for formula for calculating a sample mean is given as follows:

Sample mean = Sum of all data / Number of all data (1_

Therefore, we have:

Company A sum of all data = 9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0 = 79.50

Company A number of all data = 10

Therefore, we have:

Company A sample mean = 79.50 / 10 = 7.95

Company's B sum of all data = 11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6 = 102.60

Company B  number of all data = 10

Therefore, we have:

Company B sample mean = 102.60 / 10 = 10.26

(ii) Median

The median of a data set is the middle value of the data set after arranging the data in either increasing or decreasing order. Note that when the number if the data set is even number, the median is the average of the two middle number.

Arranging in increasing order, we have:

Company A data:  6.5; 6.7; 6.8; 7.0; 8.0; 8.5; 8.7; 8.8; 9.2; 9.3

The two middle number for company A are 8.0 and 8.5. Therefore, we have:

Company A median = (8.0 + 8.5) / 2 = 16.5 / 2 = 8.25

Company B data: 9.6; 9.7; 9.8; 9.9; 10.1; 10.2; 10.2; 11.0; 11.0. 11.1

The two middle number for company B are 10.1 and 10.2. Therefore, we have:

Company B median = (10.1 + 10.2) / 2 = 20.3 / 2 = 10.15

(b) Plot the data for the two companies on the same line and give your impression regarding any apparent differences between the two companies.

Note: See the attached pdf file for the line plot. In the graph, Company A data is plotted using small circle dots while Company B data is plotted using small cross dots.

From the graph, apparent differences between the two companies is that the rods steel of B appear to be more flexible than the rod steel of company A.

4(3x2y4)3/(2x3y5)4

Final result :

   27

 —————

 4x6y8

Step by step solution :

Step  1  :

Equation at the end of step  1  :

   (((3•(x2))•(y4))3)

 4•——————————————————

     ((2x3•(y5))4)  

Step  2  :

Equation at the end of step  2  :

     ((3x2 • (y4))3)

 4 • ———————————————

        24x12y20    

Step  3  :

            33x6y12

Simplify   ————————

           24x12y20

Dividing exponential expressions :

3.1    x6 divided by x12 = x(6 - 12) = x(-6) = 1/x6

Dividing exponential expressions :

3.2    y12 divided by y20 = y(12 - 20) = y(-8) = 1/y8

Equation at the end of step  3  :

       27  

 4 • ——————

     16x6y8

Step  4  :

Final result :

   27

 —————

 4x6y8