Exam 3: Describing Data: Numerical Measures

A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?

The information below shows the summary statistics of data adapted from Statistics Canada, regarding gasoline prices from urban cities across Canada. (i) This data is based on values from 17 cities. (ii. The average gas price in 2013 across the country based on this sample was $1.2356 (iii) 50% of the cities reported average gas prices over $1.23 per litre

The Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1977 to $5,100 million in 2000. What is the geometric mean annual percent increase in international passenger revenues?

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 25.99. (ii. Correct to two decimal places, the sample variance is approximately 675.25.

i. An outlier is a value in a data set that is inconsistent with the rest of the data. ii. 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. iii. 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.

Below is a summary of the size of homes for sale in Regina in 2005. The Empirical Rule would suggest that the middle 95% of the home sizes are between what two approximate values?

(i. The arithmetic mean (measure of central tendency) cannot be determined if the distribution has an open-ended class. (ii) The measure of central tendency used to determine the average annual percent increase in sales from one time period to another is the geometric mean. (iii) The smallest measure of central tendency in a positively skewed distribution is the mode.

(i. If two sets of data are in different units, we can compare the dispersion by using coefficient of variation. (ii) A sample of the homes currently offered for sale revealed that the mean asking price is $75,900, the median $70,100 and the modal price is $67,200. The standard deviation of the distribution is $5,900. The Pearson's coefficient of skewness is 2.95 (iii) The coefficient of variation is a measure of central tendency.

A research analyst wants to compare the dispersion in the price-earnings ratios for a group of common stock with their return on investment. For the price-earnings ratios, the mean is 10.9 and the standard deviation is 1.8. The mean return on investment is 25 percent and the standard deviation 5.2 percent. What is the relative dispersion for the price-earnings ratios and return on investment?

i. For salaries of $102,000, $98,000, $35,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average. ii. Extremely high or low scores do not affect the value of the median. iii. Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $9.

i. An outlier is a value in a data set that is inconsistent with the rest of the data. ii. 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. iii. A percentile divides a distribution into one hundred equal parts.

A company's human resource department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: (i) The mode is 21. (ii. The arithmetic mean is 20.4. (iii) The median is 23.

(i. If a distribution is highly skewed, the median (measure of central tendency) should be avoided. (ii) A characteristic of the population is called a parameter (iii) A sample revealed that the ages of musicians playing in small local combos are 36, 29, 37, 32, 36 and 75. The median is the most appropriate measure of central tendency to represent the ages of the musicians.

Mr. and Mrs. Jones live in a neighbourhood where the mean family income is $45,000 with a standard deviation of $9,000. Mr. and Mrs. Smith live in a neighbourhood where the mean is $100,000 and the standard deviation is $30,000. What are the relative dispersions of the family incomes in the two neighbourhoods?

What are half of the observations always greater than?

(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, 99 percent of the observations lie within plus and minus one standard deviation of the mean.

The following printout is a summary of number of bedrooms in homes for sale in Regina: What can we determine from this printout?

The mean, as a measure of central location would be inappropriate for which one of the following?

(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 largest 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 weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. What is the sample variance?