Exam 3: Describing Data: Numerical Measures

(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.

Rank the measures of dispersion in terms of their relative computational difficulty from least to most Difficulty.

(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, 68 percent of the observations lie within plus and minus one Standard deviation of the mean.

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.

Describe the shape of the age of death distribution.

Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. Find the weighted Mean hourly wage.

(i. The median 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.

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?

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?

(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.

(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 skewness is a measure of relative dispersion.

The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, Bell-shaped distribution. The arithmetic mean is 14.0 cm, and the standard deviation is 0.1 cm. About 68 percent of the outside diameters lie between what two amounts?

i. 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. 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 Higher than 85% of the rest of the students taking the test.

(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 and mode are both 21.

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.

A study of business faculty in Ontario revealed that the arithmetic mean annual salary is $72,000 And a standard deviation of $3,000. The study also showed that the faculty had been employed an Average (arithmetic mean) of 15 years with a standard deviation of 4 years. How does the relative Dispersion in the distribution of salaries compare with that of the lengths of service?

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.

A study of the scores on an in-plant course in management principles and the years of service of The employees enrolled in the course resulted in these statistics: i. Mean test score was 200 with a standard deviation of 40 ii. Mean number of years of service was 20 years with a standard deviation of 2 years. In comparing the relative dispersion of the two distributions, what are the coefficients of variation?

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.

The U.S. Department of Education reported that for the past six years 23, 19, 15, 30, 27 and 25 Women received doctorate degrees in computer and information sciences. What is the mean Arithmetic annual number of women receiving this degree?