A man runs 1 mile approximately once per weekend. He records his time over an 18-week period. The individual times and summary statistics are given in Table 1. (5 points) Table 1 One mile running time for an individual, over 18 weeks wk Time (min)(xi) wk Time (min)(xi) 1 12.80 10 11.57 2 12.20 11 11.73 3 12.25 12 12.67 4 12.18 13 11.92 5 11.53 14 11.67 6 12.47 15 11.80 7 12.30 16 12.33 8 12.08 17 12.55 9 11.72 18 11.83 1: What is the mean 1 mile running time over 18 weeks? 2: What is standard deviation of the 1 mile running time over 18 weeks? 3: Suppose the man does not run for 6 months over the winter due to snow on the ground. He resumes running once a week in the spring and records a running time = 12.97 minutes in his first week of running in the spring. ls this an outlying value relative to the distribution of running times recorded the previous year in Table 1? Why or why not? Hint: Construct a Box plot based on the data in Table 1 and assess whether this new point is an outlier.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A man runs 1 mile approximately once per weekend. He records his time over an 18-week period. The individual times and summary statistics are given in Table 1. (5 points)
Table 1 One mile running time for an individual, over 18 weeks
| wk | Time (min)(xi) | wk | Time (min)(xi) |
| 1 | 12.80 | 10 | 11.57 |
| 2 | 12.20 | 11 | 11.73 |
| 3 | 12.25 | 12 | 12.67 |
| 4 | 12.18 | 13 | 11.92 |
| 5 | 11.53 | 14 | 11.67 |
| 6 | 12.47 | 15 | 11.80 |
| 7 | 12.30 | 16 | 12.33 |
| 8 | 12.08 | 17 | 12.55 |
| 9 | 11.72 | 18 | 11.83 |
1: What is the mean 1 mile running time over 18 weeks?
2: What is standard deviation of the 1 mile running time over 18 weeks?
3: Suppose the man does not run for 6 months over the winter due to snow on the ground. He resumes running once a week in the spring and records a running time = 12.97 minutes in his first week of running in the spring. ls this an outlying value relative to the distribution of running times recorded the previous year in Table 1? Why or why not? Hint: Construct a Box plot based on the data in Table 1 and assess whether this new point is an outlier.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
