Exam 3: Describing Data: Numerical Measures

i. For salaries of $102,000, $98,000, $25,000, $106,000 and $101,000, the median would be an appropriate average. ii. There are always as many values above the mean as below it. 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.

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 1. (iii) The range for nylon carpet is $0.12 or 12 cents.

What is the relationship between the variance and the standard deviation?

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?

The closing prices of a common stock have been 61.5, 62, 61.25, 60.875 and 61.5 for the past week. What is the range?

(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

The Empirical Rule states that: (i) about 68% of the observation will lie within one standard deviation of the mean. ii. about 95% of the observations will lie within two standard deviations of the mean. iii. and virtually all (99.7%) will lie within three standard deviations of the mean.

Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?

If there are an odd number of observations in a set of ungrouped data that have been arrayed from low to high or vice versa, where is the median located?

The net sales of a sample of small stamping plants were organized into the following percent frequency distribution. What is the mean net sales (in $millions)?

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

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 $1.88. (iii) The range for polyester carpet is $1.04.

The number of students at a local university increased from 2,500 students 5000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of

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 $0.12 or 12 cents.

(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 mean is the most representative measure of central tendency.

Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. What is the standard deviation (in minutes)?

The ages of newly hired, unskilled employees were grouped into the following distribution: What is the median age?

(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.

i. If there is an even number of ungrouped values, then half of the values will be less than the median. ii. Extremely high or low scores affect the value of the median. iii. There are always as many values above the mean as below it.

For which measure of central tendency will the sum of the deviations of each value from that average always be zero?