A study was conducted on the average commuting distance of students at College. The study found that the first sample of thirty students has an average commute of 23.1 miles with a sample standard deviation of 12.47 miles. The commuting mileages for a second sample of 30 students are below. c) Use the means and standard deviations from each data set to illustrate the standard deviation method of identifying outliers (d) Find the five number summary for this sample and determine if there are any outliers. State the outlier values if they exist. Show your outlier calculations
A study was conducted on the average commuting distance of students at College. The study found that the first sample of thirty students has an average commute of 23.1 miles with a sample standard deviation of 12.47 miles. The commuting mileages for a second sample of 30 students are below.
c) Use the means and standard deviations from each data set to illustrate the standard deviation method of identifying outliers
(d) Find the
outlier values if they exist. Show your outlier calculations
(e) Explain why the average for the second sample is a better representation of the population of students
commuting to College. Which statistic from above proves this is the better value?
Answer:
c)
Identifying outliers using standard deviation:
Formula:
Mean=
Standard Deviation for Sample =
Here, n=30
Calculation table:
| X | X^2 |
| 20 | 400 |
| 34 | 1156 |
| 20 | 400 |
| 20 | 400 |
| 15 | 225 |
| 16 | 256 |
| 19 | 361 |
| 3 | 9 |
| 1 | 1 |
| 15 | 225 |
| 12 | 144 |
| 18 | 324 |
| 15 | 225 |
| 13 | 169 |
| 1 | 1 |
| 12 | 144 |
| 8 | 64 |
| 11 | 121 |
| 20 | 400 |
| 10 | 100 |
| 7 | 49 |
| 13 | 169 |
| 13 | 169 |
| 32 | 1024 |
| 7 | 49 |
| 4 | 16 |
| 63 | 3969 |
| 18 | 324 |
| 24 | 576 |
| 6 | 36 |
| 470 | =11506 |
SD== = 11.95
Now,
lower bound = =15.67-2*11.95=-8.23
Upper bound = =15.67+2*11.95 =55.24
There is only outlier 63.
Step by step
Solved in 2 steps
