Show All Your Work To Get Full Credit 116 Pts Suppose Your ✓ Solved

Show All Your Work To Get Full Credit116 Pts Suppose Your

1. Suppose your six exam grades in a course are: 52, 69, 75, 86, 86, and 92. Compute your final course grade (90-100= A, 80-89 = B, 70-79 = C, 60-69 =D, below 60 = F) using the a. Mean b. Median.

2. A teacher gives a 20-point test to 10 students. The scores are shown here. Find the percentile rank of a score of 12: 18, 15, 12, 6, 8, 2, 3, 5, 20.

3. The number of meteorites found in 10 of the United States is 89, 47, 164, 296, 30, 215, 138, 78, 48, and 39. Construct a boxplot for the data.

4. Find the sample variance and standard deviation for the amount of European auto sales for a sample of 6 years shown. The data are in millions of dollars: 11.2, 11.9, 12.0, 12.8, 13.4, 14.

5. How many different ways can a theatrical group select 2 musicals and 3 dramas from 11 musicals and 8 dramas to be presented during the year?

6. In a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there?

Paper For Above Instructions

The coursework involves various components of statistics and combinatorics that demonstrate computational skills and understanding of fundamental principles related to data analysis. Here's a detailed exploration of each task:

1. Final Course Grade Calculation

The six exam grades are: 52, 69, 75, 86, 86, and 92. We will first compute the mean and then the median of these grades to determine the final course grade.

a. Mean: To find the mean, sum all the grades and divide by the number of grades:

Mean = (52 + 69 + 75 + 86 + 86 + 92) / 6


Mean = 460 / 6 = 76.67

According to the grading scale, a mean of 76.67 corresponds to a grade of C (70-79).

b. Median: To find the median, arrange the grades in ascending order: 52, 69, 75, 86, 86, 92. The median is the average of the two middle numbers:

Median = (75 + 86) / 2 = 80.5

Thus, the median falls in the range of 80-89, which corresponds to a grade of B.

2. Percentile Rank Calculation

The scores from the 20-point test given to 10 students are: 18, 15, 12, 6, 8, 2, 3, 5, 20.

To calculate the percentile rank of a score of 12:

1. Count the number of scores below 12: The scores less than 12 are 2, 3, 5, 6, 8, and 12. This results in 6 scores.

2. Use the formula for percentile rank:

Percentile Rank = (Number of Scores Below X / Total Number of Scores) * 100


Percentile Rank = (6 / 10) * 100 = 60%

The percentile rank of a score of 12 is 60.

3. Boxplot Construction

For the meteorite data: 89, 47, 164, 296, 30, 215, 138, 78, 48, and 39, we identify key statistics for constructing a boxplot:

Step 1: Sort Data: 30, 39, 47, 48, 78, 89, 138, 164, 215, 296

Step 2: Find Quartiles:

  • Q1 (25th percentile): (47 + 48)/2 = 47.5
  • Q2 (Median, 50th percentile): (89 + 78)/2 = 83.5
  • Q3 (75th percentile): (138 + 164)/2 = 151

Step 3: Minimum and Maximum Values: Minimum = 30, Maximum = 296.

This data can be plotted on a boxplot showing the interquartile range (IQR) and any outliers (e.g., 296).

4. Sample Variance and Standard Deviation Calculation

We will calculate these for the European auto sales: 11.2, 11.9, 12.0, 12.8, 13.4, and 14:

Step 1: Calculate the Mean:

Mean = (11.2 + 11.9 + 12.0 + 12.8 + 13.4 + 14) / 6 = 12.5

Step 2: Calculate Variance:

Variance = [(11.2-12.5)² + (11.9-12.5)² + (12.0-12.5)² + (12.8-12.5)² + (13.4-12.5)² + (14-12.5)²] / (n-1)

Variance = [(1.69 + 0.36 + 0.25 + 0.09 + 0.81 + 2.25) / 5] = 1.04

Standard Deviation: σ = √Variance = √1.04 ≈ 1.02 million dollars.

5. Combinatorics of Musical and Drama Selection

To determine how many different ways the theatrical group can select 2 musicals from 11 and 3 dramas from 8, we apply the combination formula:

Combination formula: C(n, k) = n! / [k!(n-k)!]

Musicals:

C(11, 2) = 11! / [2!(11-2)!] = (11*10)/2 = 55

Dramas:

C(8, 3) = 8! / [3!(8-3)!] = (876)/(321) = 56

Therefore, the total combinations are: 55 * 56 = 3080 ways.

6. Committee Selection Combinations

In a club with 7 women and 5 men, to form a committee of 3 women and 2 men:

Women:

C(7, 3) = 7! / [3!(7-3)!] = (765)/(321) = 35

Men:

C(5, 2) = 5! / [2!(5-2)!] = (54)/(21) = 10

Total combinations for the committee: 35 * 10 = 350 ways.

Conclusion

In conclusion, through these calculations, we have successfully computed grades, percentiles, boxplots, variances, combinations in selection problems, and demonstrated an understanding of statistical principles important for analysis.

References

  • Weiss, N. A. (2016). Introductory Statistics. Pearson.
  • Scheaffer, R. L., & McClave, J. T. (2012). Statistics. Cengage Learning.
  • Moore, D. S., & McCabe, G. P. (2007). Introduction to the Practice of Statistics. W.H. Freeman.
  • Navidi, W., & Monk, N. (2016). Statistics. McGraw-Hill Education.
  • Bluman, A. G. (2017). Elementary Statistics: A Step By Step Approach. McGraw-Hill Education.
  • Freedman, D., Perskin, R., & Purves, R. (2007). Statistics. W.W. Norton & Company.
  • DeGroot, M. H., & Schervish, M. J. (2012). Probability and Statistics. Addison-Wesley.
  • Larson, R., & Farber, B. (2014). Elementary Statistics. Pearson.
  • Sullivan, M. (2013). Statistics. Pearson.
  • Hollander, M., & Wolfe, D. A. (1999). Nonparametric Statistical Methods. Wiley.

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