Question

Project #2: Chapter 3 Collect information on any quantitative variable for 30 members as you did for Mini-Project 1-1. Choose a different project this time, however Once you have collected the data, answer the following questions: a. List the data b. What is the target population for the sample you used? Be specific. c. Is your sample a random sample from this target population? Explain your answer. d. Do you think your sample is representative of this population? Explain why or why not. e. Is this an example of sampling with replacement or without replacement Explain why? f. Are the sample data discrete or continuous. Explain why? g. What is an element and a variable in this data set? h. Describe any problems you had in collecting the data and what impact it had on your sample. i. Were any of the data values in the population unusable. If yes, explain why Calculate the following for you data: 1. Mean 2. Median 3. Mode 4. Range 5. Standard Deviation 6. Coefficient of Variation 7. Quartiles 8. Interquartile Range 9. the 33 percentile 10. Make a Box-and-Whiskers Plot

Answer 1

f.

The sample data are discrete because no numbers are possible between any two whole numbers. For example, between 55 and 56, no other number or marks can be taken.

g.

Variable is marks of students.

Element is each individual mark of 30 students. So, there are 30 elements in our sample data set.

h.

One problem is that we classified strata based on different classes but we did not account for male and female students and if there is any significant difference between marks of male and female students, it could affect the sample if one gender was not sufficiently included in the sample. And the other problem would be that of outliers. However, we can deal with outliers in the sample, if required and remove them.

i.

No. Each element of the data is usable.

j.

1. Mean= 66.6

2. Median= 67

3. Mode= 40, 56, 57, 69, 88, 95 (each appeared 2 times)

4. Range= 95 - 36 = 59

5. Std deviation (sample std deviation)= 19.802

6. Coefficient of variation= (19.802/66.6)*100 = 29.73%

7. Quartiles: Q1= 49.75; Q2= Median= 67; Q3= 87.25

8. Interquartile Range= Q3 - Q1= 87.25 - 49.75= 37.50

9.

Data sorted from smallest to largest:

36,38,39,40,40,45,46,51,55,56,

56,57,57,59,65,69,69,70,75,77,

85,86,87,88,88,90,91,93,95,95

33rd pecentile: 33%*n = 0.33*30 = 9.9. Rounding to the nearest whole number m, it is 10. The 10th value from the data is(after arranging in ascending order as above is 56. Thus, 33rd percentile mark is 56.

10. Box and Whiskers Plot: