Exam 3: Describing Data: Numerical Measures

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?

(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.

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

The coefficient of variation for a set of annual incomes is 18%; the coefficient of variation for the Length of service with the company is 29%. What does this indicate?

(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 Variance of this distribution were computed, it would be measured in hours squared

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.

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 $123.56 (iii) More than 50% of the cities reported average gas prices over $1.25 per litre

(i. Based on the values of the arithmetic mean, median, and mode, the distribution is most likely Symmetrical. (ii. The arithmetic mean is 20.4. (iii) The median is 21.

The lengths of stay on the cancer floor of Community Hospital were organized into a frequency Distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The Standard deviation was computed to be 4.2 days. Determine the Pearson's coefficient of skewness.

i. The interquartile range is the average of the values of the first and third quartile. ii. An outlier is a data point that always occurs in the first quartile. 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.

AAA Heating and Air Conditioning completed 30 jobs last month with a mean revenue of $5,430 Per job. The president wants to know the total revenue for the month.

(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.

Listed below is the box plot of average earnings ratio for full-year, full-time female workers from 1999 to 2008. From this we can interpret that the distribution of average earnings for women for the years 1999- 2008 was:

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?

(i. If two sets of data are in different units, we can compare the dispersion by using coefficient of Skewness. (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 relative dispersion.

(i. If two sets of data are in different units, we can compare the dispersion by using coefficient of Variation. (ii. A study is made of the commissions paid to furniture salespersons. If the variance is computed, it Would be measured in dollars squared. (iii) The coefficient of skewness is a measure of relative dispersion.

The ages of a sample of telephones used in a small town hotel were organized into the following Table: What is the sample variance?

Referring to the histogram below, choose the best term to describe its shape.

A large oil company is studying the number of gallons of gasoline purchased per customer at self- Service pumps. The mean number of litres is 10.0 with a standard deviation of 3.0 litres. The median Is 10.75 litres. What is the Pearson's coefficient of skewness?

Referring to the printout below, describe the shape of the distribution of the corresponding Histogram.