Part -1:
Descriptive Statistics
1. The incomes for the five employees of Friend's Furniture are $18,000, $24,000, $24,000, $27,000 and $79,000. Calculate the mean and median salaries. In your opinion, which number gives a better indication of salaries?
2. Julie tells her class that she is going to disregard the lowest of the 10 quiz scores in Math 13 when she determines each student's final grade. Will this necessarily change a student's median score? Mean score? Explain.
3. The following are test results for one of my math classes:
65 91 73 56 84 45 88 73 85 96 75 88 73 72 82
The point total possible was 100. From these results find the following: (Round to 1 decimal place.)
a. Mean:
b. Mode
c. Median
d. Range
e. Standard deviation (attach work for this, or document the calculator steps you used to calculate the answer.)
4. Place these scores on a bell curve and comment on what the curve shows.
A typical bell curve grading distribution would assign a grade of:
A to scores which are more than 2 standard deviations above the mean
B to scores which are more than 1 but less than 2 std. dev. above the mean
C to scores which were within 1 standard deviation of the mean
D to scores which are more than 1 but less than 2 std. dev. below the mean
F to scores which are more than 2 standard deviations below the mean
5. As Shannon was reading the paper, she was dreaming about a trip to someplace warm! Using the weather chart to the right, answer the following questions.
High Low
Acapulco 88 71
Chihuahua 79 44
Mazatlan 84 47
Mexico City 85 61
Monterey 81 58
Puerto Vallarta 84 58
Veracruz 82 63
a. What is the range and standard deviation for the low temperatures in Mexico?
b. Do the low temperatures for Mexico form a "normal" distribution? Place the temperatures on a normal curve grid to illustrate your answer.
c. When should we pack our bags????
6. A recent Consumer Report article Jenny and Stephanie were reading reported that the mean number of gallons of gas consumed by a "typical American household" in a year is 750 and the standard deviation is 37 gallons. Assuming the data are normally distributed, what percentage of American households consume less than 713 gallons?
Part -2:
1. The students in two fourth grade classes were clocked for the time (to the nearest second) required to run completely around the school's playground. The results are as follows:
Times for Mr. Robertson's class: 56, 48, 61, 67, 72, 59, 74, 58, 47
57, 53, 48, 45, 62, 50, 53, 51, 72
Times for Ms. Grants' class: 65, 63, 78, 49, 58, 71, 56, 53, 78
67, 79, 45, 55, 54, 62, 54, 61
a. Construct a stem and leaf display with a central stem with Mr. Robertson's class on the left and Ms. Grants' class on the right. Order the leaves with the smallest leaves closest to the stem.
b. Which class had the better performance? Explain by referring to the stem and leaf plot.
2. In a survey of my current Math classes (total of 40 students), the following data was collected: 12 students are in choir, 10 are involved in athletics, 5 are either RA's or Chaplains, 8 are in Concordia Teacher Corp, and 5 have other commitments off campus.
a. Draw a bar graph displaying this data.
b. Draw a pie chart for this data. (Show the size of each central angle to the nearest degree.)
3. The Portland School district administered two year-end mathematics achievements tests to its fifth graders. The state test had a mean of 197 and a standard deviation of 13.2. The national test had a mean of 39 and a standard deviation of 2.9. (Compute the z-scores to the nearest hundredth.)
a. What is the z-score for a state score of 226?
b. What is the z-score for a national score of 45?
c. Which of the two test scores from parts a and b indicates the stronger performance? Explain.
4. Given the following results on the GRE (Graduate Record Exam) where the top row of numbers listed for each subject test shows the raw score for that subtest. The number in the second row of each column shows the national percentile.
a. Nationally, what percentage of the students scored below this student in Verbal Skills?
b. What percentage of the students scored above this student in Mathematics?