Exam 3: Describing Data: Numerical Measures

i. The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal zero. ii. If there is an even number of ungrouped values, the median is found by arranging them from low to high and then determining the arithmetic mean of the two middle values. iii. For salaries of $102,000, $98,000, $35,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average.

A sample of five flooring installers, each carrying three types of flooring, was taken and the price per square metre (to the nearest cent) was recorded for each type of flooring, as shown in the table below. (i) The standard deviation for laminate flooring is 0. (ii. The standard deviation for polyester carpet is $1.48. (iii) The range for polyester carpet is $1.04.

What is a disadvantage of the range as a measure of dispersion?

i. A percentile divides a distribution into one hundred equal parts. ii. A student scored in the 85 percentile on a standardized test. This means that the student scored lower than 85% of the rest of the students taking the test. iii. The interquartile range is the difference between the values of the first and third quartile, indicating the range of the middle fifty percent of the observations.

The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1990 to 857 in 2000. What is the geometric mean annual percent increase in the number of funds?

On a survey questionnaire, students were asked to indicate their class rank in college. If there were only four choices from which to choose, which measure(s) of central tendency would be appropriate to use for the data generated by that questionnaire item?

The weights of a sample of 100 boxes being shipped by Air France from Toronto to Paris are: (i) Correct to two decimal places, the sample standard deviation is approximately 52.98. (ii. Correct to two decimal places, the sample variance is approximately 675.25.

A sample of five flooring installers, each carrying three types of flooring, was taken and the price per square metre (to the nearest cent) was recorded for each type of flooring, as shown in the table below. (i) The range for laminate flooring is 1. (ii. The standard deviation for nylon carpet is 4.64 cents (iii) The range for nylon carpet is $0.12 or 12 cents.

i. The standard deviation is the positive square root of the variance. ii. For a symmetrical distribution, the variance is equal to the standard deviation. iii. If the standard deviation of the ages of a female group of employees is six years and the standard deviation of the ages of a male group in the same plant is ten years, it indicates that there is more spread in the ages of the female employees.

What must be the least scale of measurement for the median?

(i. The weekly sales from a sample of ten computer stores yielded a mean of $25,900; a median $25,000 and a mode of $24,500. The shape of the distribution is positively skewed (ii) For the mean (measure of central tendency), the data must be ranked before it is possible to determine it. (iii) If the sum of all the values of a distribution is divided by the number of values, the result is the arithmetic mean.

(i. The research director of a large oil company conducted a study of the buying habits of consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be -0.30. (ii) Rainbow Trout, Inc., feeds fingerling trout in special ponds and markets them when they attain a certain weight. A group of 9 trout (considered the population) were isolated in a pond and fed a special food mixture called Grow Em Fast. At the end of the experimental period, the weights of the trout were (in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121. Another special mixture, Fatso 1B, was used in another pond. The mean of the population was computed to be 126.9 grams and the standard deviation was 1.20 grams. When these data are analysed, we discover that the food resulting in a more uniform weight is Fatso 1B. (iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the standard deviation of this distribution were computed, it would be measured in hours squared

The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 cm, and the standard deviation is 0.1 cm. About 68 percent of the outside diameters lie between what two amounts?

A sample of the daily production of transceivers was organized into the following distribution. What is the mean daily production?

What is the median of 26, 30, 24, 32, 32, 31, 27 and 29?

A disadvantage of using an arithmetic mean to summarize a set of data is

A study of business faculty in Ontario revealed that the arithmetic mean annual salary is $62,000 and a standard deviation of $3,000. The study also showed that the faculty had been employed an average (arithmetic mean) of 15 years with a standard deviation of 4 years. How does the relative dispersion in the distribution of salaries compare with that of the lengths of service?

A sample of light trucks using diesel fuel revealed the following distribution based on fuel efficiency, i.e., litres per 100 km. What is the arithmetic mean in litres per 100 km?

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-seeConnectfordatafile.) What were the mean earnings for men for the years 1999-2008?

A sample of assistant professors on the business faculty at the largest college in Ontario revealed the mean annual income to be $62,000 with a standard deviation of $3,000. Using the Empirical Rule, what proportion of faculty earn more than $56,000 but less than $68,000?