The New York Yankees have had up and down seasons over the past few years. Here are the number of wins the Yankess amassed for each of the last few seasons:
| Year | Wins |
| 2008 | 89 |
| 2007 | 94 |
| 2006 | 97 |
| 2005 | 95 |
| 2004 | 101 |
| 2003 | 101 |
| 2002 | 103 |
| 2001 | 95 |
| 2000 | 87 |
| 1999 | 98 |
| 1998 | 114 |
| 1997 | 96 |
| 1996 | 92 |
| 1995 | 79 |
| 1994 | 69 |
Based on the information given above, calculate the following:
1. What is the mode (Mo) equal to?
2. What is (are) the median's location(s)?
3. What is the median's (Md) value ?
4. Calculate ΣX
5. What is n equal to?
6. Calculate the sample mean (M)
7. Based on this information, is the sample distribution positively skewed, negatively skewed, or unskewed?
8. What is the Range equal to?
9. What is the Sum of Squares (SS) equal to?
10. What is the sample variance (s2) equal to?
11. What is the sample standard deviation (s) equal to?
Use the following scores (X) to answer the questions below:
Based on the information given above, calculate the following:
1. What is the mode (Mo) equal to?
2. What is (are) the median's location(s)?
3. What is the median's (Md) value ?
4. Calculate ΣX
5. What is n equal to?
6. Calculate the sample mean (M)
7. Based on this information, is the sample distribution positively skewed, negatively skewed, or unskewed?
8. What is the Range equal to?
9. What is the Sum of Squares (SS) equal to?
10. What is the sample variance (s2) equal to?
11. What is the sample standard deviation (s) equal to?
Using the data in Example 2, add a constant to each value and then answer each of the following:
1. What is the mode (Mo) equal to?
2. What is (are) the median's location(s)?
3. What is the median's (Md) value ?
4. Calculate ΣX
5. What is n equal to?
6. Calculate the sample mean (M)
7. Based on this information, is the sample distribution positively skewed, negatively skewed, or unskewed?
8. What is the Range equal to?
9. What is the Sum of Squares (SS) equal to?
10. What is the sample variance (s2) equal to?
11. What is the sample standard deviation (s) equal to?
12. Compared to the answers from Example 2, how have the answers in Example 3 changed?
1. Mo = 95 and 101
2. There is an odd number of scores; hence, the median's location is [N + 1]/2 = [15 + 1]/2 = 8th ordinal position
3. Md = 95 (Be sure to rank =order the scores)
4. ΣX = 1410
5. n = 15
6. M = 94
7. The distribution is slightly negatively skewed, because the Mean is less than the median and the mode; thus, a few "low-win seasons" pulled the mean down.
8. Range = 114 - 69 = 45
9. SS = 1538.000
10. s2 = 102.533
11. s = √102.533 = 10.126
1. Mo = 9
2. Because there is an even number of scores, the median lies between the N/2 = 10/2 = 5th and [N+2]/2 = [10+2]/2 = 6th ordinal positions.
3.Md = (8 + 9)/2 = 17/2 = 8.5
4. ΣX = 80
5. n = 10
6. M = 8
7. The information is negatively slewed, because the mean is less than the median which is less than the mode.
8. Range = 5
9. SS = 22
10. s2 = 2.200
11. s =1.483
1. Mo = 14
2. Because there is an even number of scores, the median lies between the N/2 = 10/2 = 5th and [N+2]/2 = [10+2]/2 = 6th ordinal positions.
3.Md = (13 + 14)/2 = 27/2 = 13.5
4. ΣX = 130
5. n = 10
6. M = 13
7. The information is negatively slewed, because the mean is less than the median which is less than the mode.
8. Range = 5
9. SS = 22
10. s2 = 2.200
11. s =1.483
12. The measures of central tendency (Mean, Median and Mode) all increased by the constant (5); however, all of the measures of variability (Range, sum of squares, sample variance and sample standard deviation) did not change.