Question 1

The mode of a data set or a distribution of measurements, if it exists, is unique.

Accepted Answer

A data set can have more than one mode if two or more values appear with the same highest frequency; such a data set is called multimodal.

Question 2

When data have been grouped (as in a frequency table, a relative frequency histogram, etc.), the class with the highest frequency is called the modal class, and the midpoint of that class is taken to be the mode.

Accepted Answer

This statement is true.

Question 3

A data sample has a mean of 87, and a median of 117. The distribution of the data is positively skewed.

Accepted Answer

If the distribution is positively skewed, the median should be less than the mean. However, in this case, the median is greater than the mean which indicates that the distribution is negatively skewed.

Question 4

The times required to service customers' cars at a repair shop are skewed to the right with a mean of 2.5 hours and a standard deviation of 0.75 hours. What can be said about the proportion of cars whose service time is either less than one hour or more than four hours?

Accepted Answer

The answer of The times required to service customers' cars...

Question 5

If the sample mean is much larger than the sample median, the data set is said to be skewed to the right.

Accepted Answer

When the sample mean is much larger than the sample median, it indicates that there are extreme values in the data set that are pulling the mean towards the right side. This results in a longer tail on the right side and a skewed distribution towards the right. Hence, the statement is true.

Question 6

Two classes, one with 15 students and the other with 25 students, took the same test and averaged 85 points and 75 points, respectively. If the two classes were combined, the overall average score of the 40 students would be 80 points.

Accepted Answer

The combined average can be calculated by finding the total points scored by both classes and then dividing by the total number of students. For the class of 15 students with an average of 85 points, the total points scored would be 15 * 85 = 1275. For the class of 25 students with an average of 75 points, the total points scored would be 25 * 75 = 1875. The combined total points for both classes is 1275 + 1875 = 3150. Dividing this by the total number of students (40) gives an overall average score of 3150 / 40 = 78.75, not 80.

Question 7

Numerical descriptive measures computed from sample measurements are called statistics.

Accepted Answer

This statement is true. Statistics are measures obtained from samples, while parameters are measures obtained from populations.

Question 8

An analytical chemist wanted to use electrolysis to determine the number of moles of cupric ions in a given volume of solution. The solution was partitioned into n = 30 portions of 0.2 milliliter each. Each of the n = 30 portions was tested. The average number of moles of cupric ions for the n = 30 portions was found to be 0.185 mole; the standard deviation was 0.015 mole. Calculate the following intervals:  = ______________  = ______________  = ______________
Describe the distribution of the measurements for the n = 30 portions of the solution using Tchebysheff's Theorem.
________________________________________________________
Describe the distribution of the measurements for the n = 30 portions of the solution using the Empirical Rule.
________________________________________________________
Suppose the chemist had used only n = 5 portions of the solution for the experiment and obtained the readings 0.18, 0.21, 0.20, 0.22, and 0.18. Would the Empirical Rule be suitable for describing the n = 5 measurements?
______________
Explain.
________________________________________________________

Accepted Answer

The answer of An analytical chemist wanted to use electrolysis...

Question 9

The population mean,  , is used to estimate the sample mean,  .

Accepted Answer

The population mean is an unknown parameter that is estimated by the sample mean. Therefore, it is not possible for the population mean to be used to estimate the sample mean. The sample mean is calculated from the actual data in the sample.

Question 10

Jessica has been keeping track of what she spends to eat out. The last week's expenditures for meals eaten out were $15.69, $15.95, $16.19, $20.91, $17.49, $24.53, and $17.66. The mean amount Jessica spends on meals is $18.35.

Accepted Answer

To find the mean amount Jessica spends on meals, you add up all the expenditures and divide by the number of meals. The total expenditure is $128.42 ($15.69 + $15.95 + $16.19 + $20.91 + $17.49 + $24.53 + $17.66). Dividing this total by the 7 meals gives an average (mean) of approximately $18.35.

Question 11

A sample of basketball players has a mean height of 75 inches and a standard deviation of 5 inches. You know nothing else about the size of the data or the shape of the data distribution.
Which rule(s) can you use to describe the data?
______________
Explain.
________________________________________________________
Approximately what proportion of measurements will fall between 60 and 90?
______________
Approximately what proportion of measurements will fall between 65 and 85?
______________
Approximately what proportion of measurements will fall below 65?
______________

Accepted Answer

The answer of A sample of basketball players has a...

Question 12

A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a particular type of parasite. Counting the number of parasites per fox, the veterinarians found that 69 foxes had no parasites, 17 had one parasite, and so on. A frequency tabulation of the data is given here:  What fraction of the parasite counts fall within two standard deviations of the mean?
______________
Within three standard deviations?
______________
Do these results agree with Tchebysheff's Theorem?
______________
With the Empirical Rule?
______________

Accepted Answer

The answer of A random sample of 100 foxes was...

Question 13

Numerical descriptive measures computed from population measurements are called parameters.

Accepted Answer

Parameters are numerical descriptive measures computed from population measurements, while statistics are numerical descriptive measures computed from sample measurements.

Question 14

A distribution of measurements is relatively mound-shaped with mean 70 and standard deviation 10.
a. What proportion of the measurements will fall between 60 and 80?
______________
b. What proportion of the measurements will fall between 50 and 90?
______________
c. What proportion of the measurements will fall between 50 and 80?
______________
d. If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 80?
______________

Accepted Answer

The answer of A distribution of measurements is relatively mound-shaped...

Question 15

The mean and variance of a sample of n = 25 measurements are 80 and 100, respectively. Explain in detail how to use Tchebysheff's Theorem to describe the distribution of measurements.

Accepted Answer

The answer of The mean and variance of a sample...

Question 16

In a time study, conducted at a manufacturing plant, the length of time to complete a specified operation is measured for each on n = 40 workers. The mean and standard deviation are found to be 15.2 and 1.40, respectively.
a. Describe the sample data using the Empirical Rule.
________________________________________________________
b. Describe the sample data using Tchebysheff's Theorem.
________________________________________________________

Accepted Answer

The answer of In a time study, conducted at a...

Question 17

Mound-shaped data tend to cluster around a middle value.

Accepted Answer

Mound-shaped data, also known as bell-shaped or normal distribution, have a symmetrical curve that peaks at the middle value and tapers off towards the edges. This indicates that most of the data points are around the center, with fewer data points towards the extremes.

Question 18

The mode is generally used to describe large data sets.

Accepted Answer

The mode is useful for describing large data sets as it is the value that appears most frequently, providing insight into the most common occurrence or characteristic of the data.

Question 19

For Labrador Retriever dogs, the average weight at 12 months of age is 50 pounds with a standard deviation of 2.5 pounds. What can be said about the proportion of 12 month old Labrador Retrievers that will weigh between 46.25 pounds and 53.75 pounds?
Choose the appropriate rule: ______________
Approximately what proportion of weights will fall into the interval described above?
______________
Explain.
________________________________________________________

Accepted Answer

The answer of For Labrador Retriever dogs, the average weight...

Question 20

A sample of n = 10 measurements consists of the following values:
15 12 13 16 11 12 14 15 11 13
a. Can you use Tchebysheff's Theorem to describe this data set?
______________
Why or why not?
____________________________
b. Can you use the Empirical Rule to describe this data set?
______________
Why or why not?
____________________________

Accepted Answer

The answer of A sample of n = 10 measurements...

Quiz 2: Describing Data With Numerical Measures