I. Descriptive Statistics (Measures of Central Tendency)

A. Analyze the following situation about "Teacher Salaries" and answer the given questions. Show your complete solution (if necessary). Answers without solutions will be considered incorrect.

Teacher Salaries

The following data represent salaries (in pesos) from a private school in Tacloban City, Leyte.

10,000

11,000

11,000

12,500

14,300

17,500

18,000

16,600

19,200

21,560

16,400

107,000

Question - Tasks:

1. First, assume you work for the school board in a private school in Tacloban City and do not wish to raise taxes to increase salaries. Compute the mean, median, and mode, and decide which one would best support your position to not raise salaries.
2. Second, assume you work for the teachers' union and want a raise for the teachers. Use the best measure of central tendency to support your position.
3. Explain how outliers can be used to support one or the other position.
4. If the salaries represented every teacher in the school district, would the averages be parameters or statistics?
5. Which measure of central tendency can be misleading when a data set contains outliers? Explain.

B. In a sample of 20 kaing of mangoes, each containing 50 mangoes, the vendor found that 5, 8, 12, 3, 0, 6, 11, 7, 5, 4, 2, 9, 4, 2, 7, 9, 3, 6, 5, and 2 mangoes respectively are rotten.

1. On the average, how many mangoes per kaing are rotten?
2. How many percent of the total mangoes are rotten?
3. Construct a pie graph showing the percentage of rotten versus not rotten mangoes in 20 kaings.
4. If each mango can be sold at 20 pesos per piece, how much is the total price of the vendor for selling the mangoes that are not rotten?

II. Descriptive Statistics (Measures of Position)

Direction: Analyze the given problem below. Show your complete solution (if necessary). Answers without solutions will be considered incorrect.

Below are the scores of 35 grade 11 students in the final examinations in Mathematics.

61 76 68 82 90 68 93

45

54 54 79 83 58 75

70 63 72 72 77 50 100

72 98 90 96 83 89 86

85 95 88 91 68 65 57

Question - Tasks:

1. What value corresponds to the 40th percentile (P_40)?
2. What is the percentile rank of the score 85?
3. What value corresponds to Q_3?
4. If the passing grade is 75, how many percent of the students will fail?
5. If a grade of at least 90 is required to be included in the honor role, how many percent of the students are qualified?

III. Applications of Normal Distribution

Direction: Solve the following problems involving applications of Normal Distributions. Sketch also the graph of the Normal Curve. Show your complete solution. Answers without solution will be consider as incorrect. Strictly no erasures on your final answers.

1. On a test in Statistics, the mean is 65 and the standard deviation is 3. Assuming normality, what is the standard score of a student who receives a score of 60?
2. Kris gets a score of 85 in a Biology test and 80 in Math test. Scores in the Biology test have a mean of 75 and standard deviation of 5. Score in the Math test have a mean of 76 and standard deviation of 4. In which subject is her standing is better assuming that the scores in the two subjects are normally distributed?
3. In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what percent of the score is:

• greater than 65?
• less than 70?
• between 50 and 65?

4.The average weekly income of 1500 workers are Php1500 with a standard deviation of Php80. Assuming that the weekly incomes are normally distributed, find the number of workers who earn:

• between Php1440 and Php1640?
• equal to Php1350?