Question 1

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52 and $55. What is the median charge?

Accepted Answer

First, arrange the charges in ascending order: $45, $49, $50, $52, $55, $55. The median is the average of the two middle numbers, which are $50 and $52. Thus, the median charge is $(50 + 52) / 2 = $51.00.

Question 2

i. A value that is typical or representative of the data is referred to as a measure of central tendency. ii. The arithmetic mean is the sum of the observations divided by the total number of observations
iii. The value of the observation in the center after they have been arranged in numerical order is called the weighted mean

Accepted Answer

(i) and (ii) are both correct statements. However, (iii) is incorrect as the value in the center of the data after they have been arranged is actually the median, not the weighted mean. The weighted mean is the sum of the products of the weights and the values divided by the sum of the weights.

Question 3

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?

Accepted Answer

The median is the middle value when the numbers are written in order. The numbers in order are: 0, 0, 6, 8, 10, 14. The middle value is 8, so the median is 8.

Question 4

Production of passenger cars in Japan increased from 3.94 million in 1990 to 6.74 million in 2000. What is the geometric mean annual percent increase?

Accepted Answer

The geometric mean annual percent increase is calculated using the formula for geometric mean growth rate: $$ \text{Growth Rate} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{\text{Number of Periods}}} - 1 $$ Here, the final value is 6.74 million, the initial value is 3.94 million, and the number of periods (years) is 10 (from 1990 to 2000). Plugging these values into the formula gives: $$ \text{Growth Rate} = \left( \frac{6.74}{3.94} \right)^{\frac{1}{10}} - 1 \approx 0.055 \text{ or } 5.5\% $$

Question 5

A sample of the daily production of transceivers was organized into the following distribution.  What is the mean daily production?

Accepted Answer

To find the mean of a distribution, we add up all the values and divide by the total number of values. Using the provided frequency distribution, we can calculate the mean as follows:

(2 x 20) + (4 x 40) + (8 x 60) + (5 x 80) + (1 x 100) = 200 + 160 + 480 + 400 + 100 = 1,240
Total number of values: 20

Mean = 1,240/20 = 62

Therefore, the mean daily production is 106.4 (option D).

Question 6

During the past six months, the purchasing agent bought:  What is the weighted arithmetic mean price per ton?

Accepted Answer

The answer of During the past six months, the purchasing...

Question 7

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?

Accepted Answer

First, order the times from least to greatest: 50, 52, 57, 230. The median is the average of the two middle numbers, (52 + 57) / 2 = 54.5.

Question 8

The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1990 to 857 in 2000. What is the geometric mean annual percent increase in the number of funds?

Accepted Answer

We can use the formula for geometric mean annual percent increase, which is:

[(Ending Value/Beginning Value)^(1/number of years)] - 1

Plugging in the given values, we get:

[(857/410)^(1/10)] - 1 = 0.0765

Multiplying by 100 to get a percentage, we get a answer of 7.65. Therefore, the best choice is B.

Question 9

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

Accepted Answer

The answer of Using the information gathered for real estate...

Question 10

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?

Accepted Answer

To find the mean, add all the numbers together and divide by the total count. $23 + 19 + 15 + 30 + 27 + 25 = 139$. There are 6 numbers, so $139 / 6 = 23.166...$, which rounds to 23.2.

Question 11

A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company has made the following tabulation based on deliveries for the previous quarter.  What is the weighted mean profit per delivery?

Accepted Answer

The weighted mean profit per delivery can be calculated by multiplying the profit for each type of delivery by its corresponding proportion, summing up the products and dividing by the total proportion.

Weighted mean profit per delivery = [(30)(0.3) + (120)(0.5) + (200)(0.2)] / (0.3 + 0.5 + 0.2) 
= (9 + 60 + 40) / 1 
= 109

Therefore, the closest option is D) $97.

Question 12

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

Accepted Answer

The answer of Using the information gathered for real estate...

Question 13

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)?

Accepted Answer

The answer of The net sales of a sample of...

Question 14

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?

Accepted Answer

The weighted arithmetic mean price per share is calculated by finding the total cost of the shares and dividing by the total number of shares. For Kaiser Aluminum: 50 shares * $104 = $5200. For GTE: 100 shares * $25.25 (since 1/4 of a dollar is $0.25) = $2525. For Boston Edison: 20 shares * $9.125 (since 1/8 of a dollar is $0.125) = $182.5. The total cost is $5200 + $2525 + $182.5 = $7907.5. The total number of shares is 50 + 100 + 20 = 170. The weighted mean = $7907.5 / 170 = $46.51.

Question 15

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

Accepted Answer

The answer of The ages of newly hired, unskilled employees...

Question 16

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?

Accepted Answer

First, arrange the benefits in ascending order: $699, $826, $839, $880, $965, $1,087. The median is the average of the 3rd and 4th observations ($839 and $880), which is $859.50. Three observations ($699, $826, $839) are below this median.

Question 17

The Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1977 to $5,100 million in 2000. What is the geometric mean annual percent increase in international passenger revenues?

Accepted Answer

The answer of The Federal Aviation Administration reported that passenger...

Question 18

The U.S. Department of Education reported that for the past seven years 4,033, 5,652, 6,407, 7,201, 8,719, 11,154, and 15,121 people received bachelor's degrees in computer and information sciences. What is the arithmetic mean annual number receiving this degree?

Accepted Answer

To find the arithmetic mean, we need to add up all the numbers and then divide by the total number of years. So, adding up:
4,033 + 5,652 + 6,407 + 7,201 + 8,719 + 11,154 + 15,121 = 58,287
Dividing by 7 (the total number of years) gives us:
58,287/7 = 8,326.71
Rounding off to the nearest whole number, we get about 8,327. Therefore, the best choice is B, which is about 8,327.

Question 19

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.

Accepted Answer

The answer of Using the information gathered for real estate...

Question 20

A sample of light trucks using diesel fuel revealed the following distribution based on fuel efficiency, i.e., litres per 100 km.  What is the arithmetic mean in litres per 100 km?

Accepted Answer

The answer of A sample of light trucks using diesel...

Quiz 3: Describing Data: Numerical Measures

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52 and $55. What is the median charge?

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?

Production of passenger cars in Japan increased from 3.94 million in 1990 to 6.74 million in 2000. What is the geometric mean annual percent increase?

A sample of the daily production of transceivers was organized into the following distribution. What is the mean daily production?

During the past six months, the purchasing agent bought: What is the weighted arithmetic mean price per ton?

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?

The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1990 to 857 in 2000. What is the geometric mean annual percent increase in the number of funds?

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

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?

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

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) ?

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?

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

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 Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1977 to $5,100 million in 2000. What is the geometric mean annual percent increase in international passenger revenues?

The U.S. Department of Education reported that for the past seven years 4,033, 5,652, 6,407, 7,201, 8,719, 11,154, and 15,121 people received bachelor's degrees in computer and information sciences. What is the arithmetic mean annual number receiving this degree?

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.

A sample of light trucks using diesel fuel revealed the following distribution based on fuel efficiency, i.e., litres per 100 km. What is the arithmetic mean in litres per 100 km?