Exam 2: Describing Data With Numerical Measures

Attendance at London Symphony concerts for the past two years showed an average of 3000 people per performance, with a standard deviation of 100 people per performance. Attendance at a randomly selected concert was found to be 3290. If attendance data is mound-shaped, does the attendance at the selected concert appear to be unusual? Justify your conclusion.

Psychological Experiments In a psychological experiment, the time on task was recorded for ten subjects having a five-minute time constraint. These measurements (in seconds) were 182, 197, 207, 272, 192, 257, 247, 197, 232, and 237. -Refer to the Psychological Experiments statement. If you were writing a report to describe these data, which measure of central tendency would you use? Explain.

The sum of the squared deviations from the mean is always zero.

The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16, 14, 2, 8, 12, 12, 9, 10, 15, and 13. Calculate the z-score for the smallest and largest observations. Is either of these observations unusually large or unusually small?

If the variability of a set of data is very small, then the sample variance may be negative.

Suppose you are given the following set of sample measurements: -1, 0, 2, 6, and 6. a. Calculate the sample variance. b. Calculate the sample standard deviation. c. Calculate the range.

Since Tchebysheff's Theorem applies to any distribution, it provides a very conservative estimate of the fraction of measurements that fall into a particular interval.

A university placement office conducted a survey of 100 engineers who had graduated from a local university. For these engineers, the mean salary was computed to be $72,000 with a standard deviation of $8,000. Which of the following best characterizes the percentage of these engineers who earn either more than $96,000 or less than $48,000?

Flu Shot Eight doctors were asked how many flu shots they had given to patients this fall. The numbers of flu shots were 6, 3, 5, 24, 2, 6, 0, and 8. -Refer to Flu Shot statement. Find the median number of flu shots given.

Height of Basketball Players A sample of basketball players has a mean height of 190 cm, with a standard deviation of 12 cm. You know nothing else about the size of the data set or the shape of the data distribution. -Refer to the Height of Basketball Players statement. Can you use Tchebysheff's Theorem and/or the Empirical Rule to describe the data? Explain.

Cola Bottling When a machine dispensing cola at a bottling plant is working correctly, it dispenses a mean of 340 mL of cola per bottle, with a standard deviation of 6 mL. -Refer to the Cola Bottling statement. On a particular day, the bottling plant supervisor randomly selects two bottles from among those filled by the machine. One bottle contains 336 mL of cola, and the other contains 344 mL of cola. Based on the contents of these two bottles, what can the supervisor conclude about the machine's performance?

Which of the following describes a graphical device that displays the highest and lowest values in a data set, as well as the upper quartile, the middle value, and the lower quartile?

Parasites in Foxes A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a particular type of parasite. Counting the number of parasites per fox, the veterinarians found that 65 foxes had no parasites, 20 had one parasite, and so on. A frequency tabulation of the data is given here: -Refer to the Parasites in Foxes statement and table. What fraction of the parasite counts fall within two standard deviations of the mean? Do they fall within three standard deviations or the mean? Do these results agree with Tchebysheff's Theorem? Do they agree with the Empirical Rule?

The expression where is recognizable as the formula for which of the following measures?

Which of the following statements applies to this set of data values: 17, 15, 16, 14, 17, 18, and 22?