Exam 3: Describing Data: Numerical Measures

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 do not affect the value of the median. iii. There are always as many values above the mean as below it.

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the median earnings for men for the years 1999-2008?

The lengths of time (in minutes) several underwriters took to review applications for similar Insurance coverage are: 50, 230, 52 and 57. What is the median length of time required to review An application?

Using the Empirical Rule, about 95 percent of the monthly food expenditures are between What two amounts?

(i. The standard deviation the positive 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.

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)?

A sample of assistant professors on the business faculty at the largest college in Ontario revealed The mean annual income to be $62,000 with a standard deviation of $3,000. Using the Empirical Rule, what proportion of faculty earn more than $56,000 but less than $68,000?

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?

i. A parameter is a measurable characteristic of a sample. ii. The weighted mean is the nth root of n observations. iii. A statistic is a measurable characteristic of the population.

(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. (iii) The range is approximately 100.

Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish,C. History and English are 5 credit hour courses, Statistics a 4 credit hour course and Spanish a 3 credit hour course. If 4 grade points are assigned for an A, 3 for a B and 2 for a C, what is the weighted mean for the semester grades?

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the mean earnings for men for the years 1999-2008?

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What are the mean earnings for women for the years 1999-2008?

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 median for the distribution of number of sales per hour is 7 sales per hour. (ii. The first quartile for the distribution of number of sales per hour is 7 sales per hour. (iii) For the distribution of number of sales per hour, 50% of the observations are between 3 and 7.5.

(i. The weekly sales from a sample of ten computer stores yielded a mean of $25,900; a median $25,000 and a mode of $24,500. The shape of the distribution is positively skewed (ii. For the median (measure of central tendency), the data must be ranked before it is possible to Determine it. (iii) If the sum of all the values of a distribution is divided by the number of values, the result is the Arithmetic mean.

i. A percentile divides a distribution into one hundred equal parts. ii. 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. iii. 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.

A stockbroker placed the following order for a customer: -50 shares of Kaiser Aluminum preferred at $104 a share -100 shares of GTE preferred at $25 1/4 a share -20 shares of Boston Edison preferred at $9 1/8 a share What is the weighted arithmetic mean price per share?

A large group of inductees was given a mechanical aptitude and a finger dexterity test. The Arithmetic mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The mean and standard deviation for the finger dexterity test were 30 and 6 respectively. What is The relative dispersion in the two groups?

(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 standard deviation is Computed, it would be measured in dollars squared. (iii) The coefficient of variation is a measure of relative dispersion.