Exam 3: Describing Data: Numerical Measures

What is the range for this sample of March electric bills amounts for all-electric homes of similar sizes (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and $194.

i. For salaries of $102,000, $98,000, $25,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average. ii. Extremely high or low scores 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 $10.

(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 relative dispersion.

A sample of single persons receiving social security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839 and $965. How many observations are below the median?

The net incomes (in $millions) of a sample of steel fabricators are: $86, $67, $86 and $85. What is the modal net income?

The annual incomes of the five vice presidents of Elly's Industries are: $41,000, $38,000, $32,000, $33,000 and $50,000. The annual incomes of Unique, another firm similar to Elly's Industries, were also studied and found to have a mean of $38,900 and a standard deviation of $6,612. Determine the coefficient of variation for each firm.

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 are the mean earnings for women for the years 1999-2008?

(i. A small manufacturing company with 52 employees has annual salaries distributed such that the mean is $25,459, the median is $24,798 and the mode is $24,000. An additional foreman is hired at an annual salary of $50,700. The measure of central tendency that is most affected by the addition of this salary is the arithmetic mean. (ii) In the relationship between the mean and median in a negatively skewed distribution the mean is less than the median. (iii) In the relationship between the median and the mode in a positively skewed distribution, the median is smaller than the mode.

Which measure of central tendency is found by arranging the data from low to high, and selecting the middle value?

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. A small manufacturing company with 52 employees has annual salaries distributed such that the mean is $25,459, the median is $24,798 and the mode is $24,000. An additional foreman is hired at an annual salary of $50,700. The measure of central tendency that is most affected by the addition of this salary is the arithmetic mean. (ii) In the relationship between the mean and median in a negatively skewed distribution the mean is less than the median. (iii) In the relationship between the median and the mode in a positively skewed distribution, the median is greater than the mode.