Chapter 2: 140SE (page 142)
Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.
When there is skewness in the data set.
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Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.
| Tally for Discrete Variables: DRIVSTAR | ||
DRIVSTAR | Count | Percent |
2 3 4 5 N = | 4 17 59 18 98 | 4.08 17.35 60.20 18.37 |
| Descriptive Statistics: DRIVHEAD | ||||||||
Variable | N | Mean | StDev | Minimum | Q1 | Median | Q3 | Maximum |
DRIVHEAD | 98 | 603.7 | 185.4 | 216.0 | 475.0 | 605.0 | 724.3 | 1240.0 |
C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.
d..Find the z-score for a driver head-injury rating of 408. Interpret the result.
Calculate the range, variance, and standard deviation for the following samples:
a.39, 42, 40, 37, 41
b.100, 4, 7, 96, 80, 3, 1, 10, 2
c.100, 4, 7, 30, 80, 30, 42, 2
Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of transformer voltage sags and swells, Exercise 2.76 (p. 110). Recall that for a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.
a. Find the z-score for the number of sags for this transformer. Interpret this value.
b. Find the z-score for the number of swells for this transformer. Interpret this value.
Calculate the mode, mean, and median of the following data:
18 10 15 13 17 15 12 15 18 16 11
A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements are outliers.
a.65
b.21
c.72
d.98
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