Statistics Assignment
Assignment 5
Please show the processes
Question 1: (You need to use Table A.1 , attached with the question)
A group of Widener students took the math101 midterm test, the mean score is 40, and standard deviation is 8.
John’s Z score is -.50, Emily’s Z score is 0, Fred’s Z score is 0.25, and Kate’s Z score is 1.25.
- What are the percentile ranks of John’s, Emily’s, Fred’s, and Kate’s scores respectively?
- Who performed best in this test?
- Except for mean score, why it is also important to know the standard deviation to understand each individual score?
Question 2: You need to use Table A.1, attached with the question)
Assume that a set of 300 scores in normally distributed with a mean of 60 and a standard deviation (SD) of 20
- What are the Z scores corresponding to the raw scores of 100, 60, and 45?
- How many scores lies between 45 and 100?
- How many scores exceed the score of 100?
- How many scores are less than the score of 45?
- Find the percentile ranks of the score of 100, 60, and 45.
Question. 3
The following data is a sample of the data taken from the Behavioral Risk Factor Surveillance System survey from 2010 (http://www.cdc.gov/brfss/). There are 80 male participants in this sample. The first table provides the descriptive statistics for the weight variable, while the second table provides the individual Z scores associated with each participant in the sample.
There are two parts to this assignment.
- Describe the descriptive data for the weight variable in the first table. Such as, what is the mean, range, etc.
- Identify the case with the largest Z-score for the weight variable presented in the second table and provide an interpretation of this score: for example, is this score above the mean? if it is above, how much it is above respective to Standard Deviation (SD)? What is the raw score of weight for this participant?
- Identify the case with the lowest Z-score for the weight variable presented in the second table and provide an interpretation of this score: for example, is this score above the mean? if it is above, how much it is above respective to Standard Deviation (SD)? What is the raw score of weight for this participant?
- For ID80, the Z score for the weight is 0.02, what does this Z score tell you? For example, is the weight of this participant close to Mean 203.98? How do you know?
Table 1. Descriptive Statistics
| Descriptive Statistics | |||||||
| N | Range | Minimum | Maximum | Mean | Std. Deviation | Variance | |
| WEIGHT2 REPORTED WEIGHT IN POUNDS | 80 | 250 | 135 | 385 | 203.98 | 42.509 | 1806.987 |
| Valid N (listwise) | 80 | ||||||
Table 2. Z Scores
| ID | ZWEIGHT | IDNUM | ZWEIGHT | ID | ZWEIGHT | ||
| 1 | -1.62 | 31 | 0.21 | 61 | -0.09 | ||
| 2 | -0.09 | 32 | 4.26 | 62 | 1.79 | ||
| 3 | 1.08 | 33 | -0.56 | 63 | -0.45 | ||
| 4 | -0.96 | 34 | -1.39 | 64 | -1.03 | ||
| 5 | 0.85 | 35 | 0.85 | 65 | -0.96 | ||
| 6 | -0.45 | 36 | -0.68 | 66 | 1.44 | ||
| 7 | -0.45 | 37 | -0.33 | 67 | -0.14 | ||
| 8 | -0.35 | 38 | 0.14 | 68 | -0.71 | ||
| 9 | -0.33 | 39 | -0.92 | 69 | 1.44 | ||
| 10 | -0.14 | 40 | -1.03 | 70 | 2.26 | ||
| 11 | -0.09 | 41 | -0.09 | 71 | 0.38 | ||
| 12 | 0.42 | 42 | 2.85 | 72 | 0.42 | ||
| 13 | 1.08 | 43 | 0.17 | 73 | -0.33 | ||
| 14 | -0.33 | 44 | -0.33 | 74 | -0.28 | ||
| 15 | -1.27 | 45 | -0.68 | 75 | -1.27 | ||
| 16 | 0.85 | 46 | -0.33 | 76 | -1.03 | ||
| 17 | -0.59 | 47 | 1.08 | 77 | 0.85 | ||
| 18 | 1.32 | 48 | 0.85 | 78 | -0.92 | ||
| 19 | 0.49 | 49 | -0.56 | 79 | -0.28 | ||
| 20 | -1.39 | 50 | -0.80 | 80 | 0.02 | ||
| 21 | -0.56 | 51 | 0.85 | ||||
| 22 | -0.05 | 52 | -0.40 | ||||
| 23 | 1.08 | 53 | -1.22 | ||||
| 24 | -0.45 | 54 | -0.33 | ||||
| 25 | -0.09 | 55 | 0.07 | ||||
| 26 | -0.68 | 56 | -0.21 | ||||
| 27 | -0.85 | 57 | -0.42 | ||||
| 28 | 0.61 | 58 | -0.56 | ||||
| 29 | 0.38 | 59 | -0.56 | ||||
| 30 | 1.67 | 60 | -0.09 |
