Exam 3: Describing Data: Numerical Measures

(i. The standard deviation the positive square root of the variance. (ii) The capacities of several metal containers are: 38, 20, 37, 64, and 27 litres. The range in litres is 44. (iii) The sum of the deviations of each value from the mean equals zero.

(i. The mean is the measure of central tendency that uses all of the observations in its calculation. (ii) The mode is the class with the fewest number of observations. (iii) If a set of observations contains an extreme value and none of the observations repeat themselves, the median is the most representative measure of central tendency.

The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41 and 22. What is the population variance?

Below is a summary of the size of homes for sale in Regina in 2005. The Empirical Rule would suggest that the middle 68% of the home sizes are between what two approximate values?

i. In a positively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve. iii. In a negatively skewed distribution, the mode is greater than the median.

(i. Five students were given a page of problems with the instructions to solve as many as they could in one hour. Five students solved the following number of problems: 12, 10, 8, 6 and 4. The arithmetic mean number of minutes required per problem is 7.5 minutes (average of 8 problems in an hour). (ii) David Electronics had a profit of $10 million in 1998. Profit doubled from 1998 to 1999 and profit increased eight fold from 1999 to 2000. The annual geometric mean rate of growth from 1998 to 2000 was 300% (4 fold). (iii) The difference between the highest and the lowest value in a set of data is called the range.

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: Determine the age of the youngest person who died in this sample.

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the median of the selling prices at that time.

A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company has made the following tabulation based on deliveries for the previous quarter. What is the weighted mean profit per delivery?

Which of the following measures of dispersion are based on deviations from the mean?

(i. If the mean of a frequency distribution is smaller than the median and mode, the Pearson's coefficient of skewness would be negative. (ii) The only time the variance equals the standard deviation is when both equal 1. (iii) According to the Empirical Rule, 90 percent of the observations lie within plus and minus one standard deviation of the mean.

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What are the median earnings for women for the years 1999-2008?

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 modal earnings for men for the years 1999-2008?

A large group of inductees was given a mechanical aptitude and a finger dexterity test. The arithmetic mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The mean and standard deviation for the finger dexterity test were 30 and 6 respectively. What is the relative dispersion in the two groups?

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 0 or none. (ii. The variance for laminate flooring is 0. (iii) The range for nylon carpet is $0.12 or 12 cents.

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: Determine the age of the oldest person who died in this sample.

(i. The standard deviation the negative square root of the variance. (ii) The capacities of several metal containers are: 38, 20, 37, 64, and 27 litres. The range in litres is 44. (iii) The sum of the deviations of each value from the mean equals zero.

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 0 or none. (ii. The mean deviation for laminate flooring is 0. (iii) The range for nylon carpet is $0.12 or 12 cents.

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 0 or none. (ii. The standard deviation for nylon carpet is 4.64 cents (iii) The range for nylon carpet is $0.15 or 15 cents.

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000s, determine the mean of the selling prices at that time.