Exam 2: Describing Data With Numerical Measures

A sample of 2,500 vehicles in Minnesota showed the following statistics related to the number of accidents per month: Based on these data, we can infer that the distribution accidents is skewed.

Numbers that indicate the spread or scatter of observations in a data set are:

The Empirical Rule states that: Given a distribution of measurements that is approximately bell-shaped (mound-shaped), the interval contains approximately 68% of the measurements, the interval contains approximately 95% of the measurements, and the interval contains all or almost all of the measurements.

A student scores 89, 75, 94, and 88 on four exams during the semester and 97 on the final exam. If the final is weighted double and the four others weighted equally, the student's final average would be 90.

Thirty-three students were asked to rate themselves on whether they were outgoing or not using this five point scale: 1 = extremely extroverted, 2 = extroverted, 3 = neither extroverted nor introverted, 4 = introverted, or 5 = extremely introverted. The results are shown in the table below: a. Calculate the sample mean. ______________ b. Calculate the median. ______________ c. Calculate the sample standard deviation. ______________

The lengths of screws produced by a machine are normally distributed with a mean of 3 inches and a standard deviation of .2 inches. Therefore, we know:

A sample of eight doctors was 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. a. Find the sample mean. ______________ b. Find the sample median. ______________ c. Based on the values of the mean and median in parts (a) and (b) above, are the measurements symmetric or skewed? ______________ Explain. ________________________________________________________

The variance is:

The distribution of dollars paid for home insurance by home owners in Detroit is bell - shaped with a mean equal to $800 every six months, and a standard deviation equal to $120. Based on this information, we can use Tchebysheff's Theorem to determine the percentage of home owners that will pay between $560 and $1,040 for home insurance.

When a machine dispensing cola at a bottling plant is working correctly, it dispenses a mean of 12 ounces of cola per bottle with a standard deviation of 0.2 ounces. a. When the machine is working correctly, what percentage of the bottles will be filled with between 11.6 and 12.4 ounces of cola? At least ______________. b. On a particular day, the bottling plant supervisor randomly selects two bottles from among those filled by the machine. One bottle contains 11.8 ounces of cola, and the other contains 12.1 ounces of cola. Based on the contents of these two bottles, what can the supervisor infer (conclude) about the machine's performance? ____________________________

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?

z-scores exceeding 3 in absolute value are likely to occur.

You are given the following measurements: 0.10, 0.25, 0.20, 0.15, and 0.16. a. Multiply each of the values by 100, and calculate the sample mean for the new data. ______________ b. Without actually calculating the sample mean, what was the mean of the original data? ______________

The distribution of actual weight of tomato soup in a 16 ounce can is thought to be bell-shaped with a mean equal to 16 ounces, and a standard deviation equal to 0.25 ounces. Based on this information, between what two values could we expect 95% of all cans to weigh?

The following data represent the number of calories in 12 ounce cans of eight popular soft drinks: 124 144 147 146 148 154 150 234 a. Find the median. ______________ b. Find the sample mean. ______________ c. Based on the values in parts (a) and (b) above, are the measurements symmetric or skewed? ______________ Explain. ________________________________________________________

A data set in which the mean and median are equal is said to be bimodal data.

A student took a chemistry exam where the exam scores were mound-shaped with a mean score of 90 and a standard deviation of 64. She also took a statistics exam where the scores were mound-shaped, the mean score was 70 and the standard deviation was 16. If the student's grades were 102 on the chemistry exam and 77 on the statistics exam, then:

Which of the following represents a disadvantage of using the sample range to measure spread or dispersion?

The following data represent a sample of 10 scores on a 20-point statistics quiz: 16, 16, 16, 16, 16, 18, 18, 20, 20, and 20. After the mean, median, range and variance were calculated for the scores, it was discovered that one of the scores of 20 should have been an 18. Which of the following will change when the calculations are redone using the correct scores?

Which of the following statements about the median is correct?