Exam 3: Describing Data: Numerical Measures

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: Describe the shape of the age of death distribution. (i. Since the mode is the largest of the 3 measures of central tendency, more people died at this older age than any earlier age (ii. Since the mean age of death is the lowest of the three measures of central tendency, there must have been one or more person who died at a significantly younger age than the mode (iii) Since the mode is the largest of the 3 measures of central tendency, everyone died at this age

A telemarketing firm is monitoring the performance of its employees based on the number of sales per hour. One employee had the following sales for the last 20 hours (i) The median for the distribution of number of sales per hour is 6 sales per hour. (ii. The first quartile for the distribution of number of sales per hour is 4 sales per hour. (iii) For the distribution of number of sales per hour, 50% of the observations are between 4 and 6.5.

A company's human resource department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: (i) The mode is 21. (ii. The arithmetic mean is 20.4. (iii) The median is 21.

The number of work stoppages in a highly industrialized region for selected months are: 6, 0, 10, 14, 8 and 0. What is the median number of stoppages?

(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 5.20 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

A company's human resource department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: (i) The mode is 3. (ii. The arithmetic mean is 20.4. (iii) The median is 21.

Samples of the wires coming off the production line were tested for tensile strength. The statistical results (in PSI) were: According to the Empirical Rule, the middle 95 percent of the wires tested between approximately what two values?

What disadvantage(s) are there of the mean deviation?

A disadvantage of using an arithmetic mean to summarize a set of data is

What is the relationship among the mean, median and mode in a symmetric distribution?

(i. If a distribution is highly skewed, the mean (measure of central tendency) should be avoided. (ii) A characteristic of the population is called a parameter (iii) A sample revealed that the ages of musicians playing in small local combos are 36, 29, 37, 32, 36 and 75. The median is the most appropriate measure of central tendency to represent the ages of the musicians.

A sample of the daily number of passengers per bus riding the Bee Line commuter route yielded the following information: What is the standard deviation?

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000s, determine the standard deviation of the selling prices at that time.

Which measure of central tendency is used to determine the average annual percent increase?

If a major sports star were to move into your neighbourhood, what would you expect to happen to the neighbourhood's "average" income?

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.

(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 3.95 (iii) The coefficient of variation is a measure of relative dispersion.

In order to predict life expectancy, a data sample is received from a local funeral parlour. The sample includes the ages (in years) of each of the customers received over the past few weeks. The following is the Excel summary statistics: What is the size of the sample?

(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.

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 were the modal earnings for women for the years 1999-2008?