Question

1. (8 pts.) PBS (Sept. 6, 2010) cited a report (Organisation for Economic Co-operation and Development) examining both the speed and cost of the Internet. PBS reported the following: "Japan has the fastest average connection speed at 61 megabits per second and the lowest monthly connection price (per mbps) at $0.27. The United States ranked 15th with an average connection of 4.8 mbps and monthly price (per mbps) of $3.33." Below are the updated data for 2012 (adapted slightly for this assignment). The first column is the cost mbps and the second column includes the cost inclusive of the line charges.

                                         Cost MBPS    Total Cost/Month

Mexico	1.69	58.98
Greece	1.25	16.72
Turkey	1.12	48.98
Chile	0.96	19.28
Israel	0.77	11.78
New Zealand	0.65	130.20
Italy	0.64	6.93
Ireland	0.61	47.17
Belgium	0.59	28.93
Austria	0.56	5.05
United States	0.53	41.70
Luxembourg	0.52	10.56
Switzerland	0.47	58.06
Portugal	0.46	6.27
Norway	0.46	18.02
Poland	0.45	127.12
Iceland	0.42	6.75
Germany	0.40	23.25
Czech Republic	0.40	12.35
United Kingdom	0.39	2.12
Canada	0.39	9.86
Denmark	0.36	1.79
Australia	0.34	6.81
Hungary	0.30	26.67
France	0.23	5.10
Korea	0.22	2.07
Finland	0.22	15.99
Sweden	0.11	18.63
Netherlands	0.08	4.52
Japan	0.04	21.34

Find the mean, median, and mode for the data for the cost MBPS.

          Mean =                            Median =                            Mode = ___________                   

Find the range, standard deviation, and variance for these data.

          Range =                               S =                                S2 =  ____________         

Find the mean, median, and mode for these data for the total monthly cost inclusive of the line charges.

           Mean =                            Median =                            Mode = ___________                   

  

Find the range, standard deviation, and variance for these data.

           Range =                               S =                                S2 =  ____________         

Write a short email describing the results of this study to a friend. Remember to convey the results of the study particularly in relation to variability. What does this study tell you about Internet costs around the globe?

2. (5 pts.) Iron levels for a sample of adult women on a vegan diet are recorded below (normal iron levels: women 40-150; men 50-175 mcg/dL).

65

           115

146

           117

95

           108

           132

           127

             86

             48

85

           117

126

           117

             98

           118

           111

           123

             85

             43

   Find the mean, median, and mode for the data.

        Mean =                             Median =                          Mode =  ___________                 

Find the range, standard deviation, and variance for the data.

         Range =                                 S =                               S2 =  ___________                   

You have a friend who has just decided to become a vegan. What would you tell your friend?

3. (2 pts.) Find the area between the following z-scores.

   Answer                  : z = 0 and z = 1.45

   Answer                  : z = 0 and z = 1.67

   Answer                  : z = -.96 and z = 0

   Answer                  : z = -1.92 and z = 0

4. (2 pts.) Find the area between the following z-scores

   Answer                 : z = -1.4 and z = .8

   Answer                 : z = -2.8 and z = 1.73

   Answer                 : z = -1.6 and z = -.35

   Answer                : z = 1.3 and z = 1.92

5. (3 pts.) Students completed an exam with a mean = 50 and a standard deviation of 8. Using this information, answer each of the questions below.

   Answer                 : Clem received a score of 56 on the test. What percentage of students scored less than Clem?

   Answer                 : Ewald received a score of 40 on the test. What percentage of students scored higher than Ewald?

   Answer                 : Roscoe received a score of 45 on the test. What percentage of students scored higher than Roscoe?

   Answer                 : Myrtle received a score of 47 on the test. Buford received a score of 54 on the test. What percentage of student scored between Myrtle and Buford?

Answer 1

1) Mean, Median, Mode for data of cost MBPS:

Mean:

sample size is 30. Mean is defined as sum of all values divided by sample size. Here sum of all 30 values of cost MBPS is 15.63

Median:

Median is middle value of the ordered data set. From table we can see that values in column cost MBPS are already ordered from maximum to minimum.

Middle values are 15th and 16th values. i.e. Norway and Poland

Median is the average of these two values:

Mode:

Mode of the data set is most repeated value.

From table we can see that this is multimodal data.

Because 0.46, 0.4, 0.39 and 0.22 all these values are repeated twice. No other value is repeated more than twice.

Thus there are 4 mode values: 0.46, 0.4, 0.39 and 0.22

2) Range, standard deviation and variance for the cost MBPS:

Standard deviation of the data is given by the formula (data is considered as a sample):

We have,

n = 30,

To find find square of all values in column of cost MBPS and add them up.

Plugging in all values into the formula we get,

Variance:

Variance is the square of standard deviation:

Hence,

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1) Mean, Median, Mode for data for the total monthly cost inclusive of the line:

Mean:

sample size is 30. Mean is defined as sum of all values divided by sample size. Here sum of all 30 values of total cost is 793.

Median:

Median is middle value of the ordered data set. This column in not ordered. Therefore we first need to order data set.

Ordered data set from largest to smallest:

130.2, 127.12, 58.98, 58.06, 48.98, 47.17, 41.7, 28.93, 26.67, 23.25, 21.34, 19.28, 18.63, 18.02, 16.72, 15.99, 12.35, 11.78, 10.56, 9.86, 6.93, 6.81, 6.75, 6.27, 5.1, 5.05, 4.52, 2.12, 2.07, 1.79

Middle values are 15th and 16th values. i.e. Greece(16.72) and Finland (15.99)

Median is the average of these two values:

Mode:

No value is repeated in this data set. Therefore there is no mode for this data.

2) Range, standard deviation and variance for the data of total monthly cost inclusive of the line:

Standard deviation of the data is given by the formula (data is considered as a sample):

We have,

n = 30,

To find find square of all values in column of total cost and add them up.

Plugging in all values into the formula we get,

Variance:

Variance is the square of standard deviation:

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Total cost of the internet per month varies a lot as compared to the variation in the cost MBPS.

There is a huge difference in the range, standard deviation and variances of the cost MBPS and total cost.