It's high school level technically.Module 2 V. Demydovych, Summer 2021 Module 2 Assignment 1....

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It's high school level technically.Module 2 V. Demydovych, Summer 2021 Module 2 Assignment 1. Consider the following data set: 0.04 0.10 -0.05 -0.02 0.08 0.15 -0.09 (a) Calculate and interpret the 25th, 50th, and 75th percentiles. (b) Construct a box plot. Are there any outliers? 2. Consider the following sample data: -10 12 -8 -2 -6 8 (a) Calculate the range. (b) Calculate the MAD. (c) Calculate the variance and the standard deviation. 3. A data set has a mean of 80 and a standard deviation of 5. (a) Using Chebyshev’s theorem, what percent of the observation fall between 70 and 90? (b) Using Chebyshev’s theorem, what percent of the observation fall between 65 and 95? 4. Consider a bell-shaped distribution with a mean of 750 and a standard deviation of 50 . There are 500 observations in the data set. (a) Approximately what percent of the observations are less than 700? (b) Approximately how many observations are less than 700? 5. Consider the following frequency distribution: Class Frequency 50 up to 60 10 60 up to 70 15 70 up to 80 8 80 up to 100 2 (a) Calculate the sample mean. (b) Calculate the sample variance. (c) Calculate the sample standard deviation. 6. A social scientist wants to analyze the relationship between educational attainment and salary. He interviews eight people. Consider the following results: Education 3 4 6 2 5 4 8 0 Salary 40 53 60 35 55 50 80 35 (a) Calculate the covariance. What kind of linear relationship exists? (b) Calculate and interpret the correlation coefficient. 7. Consider the following sample data: x -30 10 0 23 16 y 44 -15 -10 -2 5 Module 2 V. Demydovych, Summer 2021 (a) Construct and interpret a scatter plot. (b) Calculate and interpret Sxy. (c) Calculate and interpret rxy. 8. Consider the following sample data: x 12 23 11 23 14 21 18 16 y 28 43 21 40 33 41 37 32 (a) Construct a scatter plot and verify that estimating a simple linear regression model is ap- propriate in this problem. (b) Calculate slope and intercept. What is the sample regression equation? (c) Find the predicted value of y if x equals 10, 15, and 20.

Suraj · Accepted Answer

Solution 1:
Consider the given data set,
0.04, 0.10, -0.05, -0.02, 0.08, 0.15, -0.09
(a)
Since there are total 7 observations.
Thus, arrange the values in ascending order as follows:
-0.09, -0.05, -0.02, 0.04, 0.08, 0.10, 0.15
25th percentile
                        
Thus, 2nd observation -0.05 is 25th percentile.
50th percentile
                        
Thus, 4th observation 0.04 is 50th percentile.
75th percentile
                        
Thus, 5nd observation 0.08 is 75th percentile.
(b)
The boxplot for the data is given as follows:
There is no outlier in the boxplot.
Solution 2:
Consider the given data as follows:
-10, 12, -8, -2, -6, 8
(a)
Range
           
(b)
Let A = -8
MAD
          
Thus, MAD is 10.33.
(c)
Variance
               
Standard deviation
                               
Solution 3:
Mean = 80
Standard deviation (sd) = 5
(a)
First find the value of k.
Mean – k(sd) = lower limit
80 - 5K = 70
80 - 70 = 5k
10 = 5k
K = 2
To get the percentage use .
Hence, 75% of the data set lies between 70 and 90.
(b)
First find the value of k.
Mean – k(sd) = lower limit
80 - 5K = 65
80 - 65 = 5k
15 = 5k
K = 3
To get the percentage use .

Module 2 V. Demydovych, Summer 2021 Module 2 Assignment 1. Consider the following data set: XXXXXXXXXX XXXXXXXXXX (a) Calculate and interpret the 25th, 50th, and 75th percentiles. (b) Construct a box...

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