RSCH 665 – Module 2 Assignment

Measures of Central Tendency and Variability

1. One semester, a statistics professor gave six exams to the class. In an effort to get the students to apply what they have learned in their statistics classes, they are told that the final course grade for each student will be based on the central tendency measurement of their choice. Below are the scores for three of the students. Calculate the mean, mode and median for each student and present in a table. Which measure of central tendency would you suggest that each one choose?

	Examination
	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6
Emmett	94	74	63	59	74	92
Kiernan	84	83	73	80	88	80
Brennan	92	68	69	82	92	78

Emmett?  

Kiernan?

Brennan?

Measures of Variance and Standard Deviation

2. As part of an assessment for navigation, a professor has his students take a written test. He teaches five sections of the class. The scores from the students in each section appear below. Compute the mean, variance, and standard deviations for each class shown below in the table. **Assume these students are the entire population. (This is a clue – check your StatCrunch videos for the differences in how to calculate standard deviation for a sample and a population.)

Class	Student Scores
	A	B	C	D	E	F	G	H	I
1	94	84	74	54	84	92	71	63	92
2	89	79	84	77	79	73	77	71	96
3	93	92	91	87	84	88	81	73	77
4	85	74	93	91	93	98	94	70	86
5	82	100	85	78	68	68	99	90	90

Class 1:

Class 2:

Class 3: 

Class 4: 

Class 5: 

3. Below in the table is the data from Set 1 of training 24 airport security guards. In this study, participants were asked to identify security risks. The researcher recorded how many they identified. Assume this data reflects a sample. Calculate the mean, variance, and standard deviation for this set of scores. Explain the difference between the standard deviation of these scores (a sample) and standard deviation of a population.

Risks Identified
9	16	14	10	24	5	25	19
18	32	7	18	38	7	22	11
7	14	1	3	12	16	23	10

The table below will be used for the following five questions. The table represents the mean and standard deviation graduation rates, by candidate age, for a population of flight academies. Here is an electronic version of the Z-table. (Each subquestion = 5 points for a total of 25 points)

Age	Mean Graduation Rate	Standard Deviation
16	75.6	1.8
17	80	2.1
18	78.5	1.4
19	78.6	2.5
20	82.2	2.5
21	85.2	2.2
22	86.5	2.0
23	89.5	1.2
24	87.5	1.8
25	86.7	1.7
26	87.8	1.3
27	87.1	1.9
28	88.8	2.8
29	91.1	1.0
30	84.8	2.8
31	87.3	2.2
32	87.3	1.4
33	82.5	2.0
34	83.1	1.3
35	89.1	1.7
36	88.2	1.7
37	85.5	1.2
38	81.5	2.0
39	84.8	1.9
40	84.4	1.6

1. A flight academy has a graduation rate of 72.1 among all their 17-year old candidates from the last five years. What percentage of flight academies have a higher graduation rate for 17-year old candidates?

• A flight academy has a graduation rate of 83.5 among all their 34-year old candidates from the last eight years. What percentage of flight academies have a lower graduation rate for 34-year old candidates?

• A flight academy boasts it is among the top 10% for graduation rates among its 29-year old candidates. This academy’s graduation rate is 93.1 over the last two years for 29-year old candidates. Is the claim that this flight academy is in the top 10% a true statement? Explain.

• A flight academy wants to invest in new training methods to improve its graduation rate of 18-year old candidates. This academy’s graduation rate for 18-year old candidates is 82.6 for the past ten years. Should the academy invest in the new training methods?  Explain.

• A flight academy had a graduation rate of 85.1 for 27-year old candidates from 2000-2009. Since then, new instructors have been hired that have specifically worked on providing clearer instruction to pilot candidates. From 2010-2018, the graduation rate for 27-year old candidates is 88.3. What percentile did the organization start at from 2000-2009, and what percentile is the organization now (2010-2018)?  Explain what this means in terms of percentage of population between these scores.