Question 1

Calculate  for the following sample data set: ​  ​

Accepted Answer

A

Question 2

What is the smallest possible value for a sample standard deviation?

Accepted Answer

The smallest possible value for a sample standard deviation is 0, which occurs when all the values in the sample are identical, resulting in no variability among them.

Question 3

The following is an abbreviated list of scores from a recent exam.Which exam score is the 15th percentile?

Accepted Answer

To find the 15th percentile, we need to arrange the scores in order from lowest to highest and then find the value that corresponds to the 15th percentile. In this case, the order would be: 28, 32, 43, 45, 47, 51, 53, 55, 56, 57, 64, 89, 98, 100. The 15th percentile corresponds to the score that is greater than or equal to 15% of the other scores. Using a calculator or a percentile chart, we find that the score is 35.6, which is closest to 28. Therefore, the answer is B.

Question 4

The sample mean is:

Accepted Answer

The sample mean is calculated using the values in a specific sample, so it will vary from sample to sample. It is not the same for all distributions. It is a measure of central tendency, not a measure of spread, so D is not correct. C is also not correct because the sample mean can be calculated and is not unknowable.

Question 5

Calculate s2 for the following sample data set: ​  ​

Accepted Answer

The answer of Calculate s2 for the following sample data...

Question 6

A personnel manager believes that a particular employee produces more defective parts than his peers.The manager records the worker's production over the course of several weeks.Out of 315 parts produced, 11 are defective.Calculate  (the sample proportion) if we define a defective part as a "success."

Accepted Answer

The sample proportion is calculated by dividing the number of successes (defective parts) by the total number of observations (parts produced). In this case, the sample proportion is 11/315, which simplifies to 0.035. Therefore, the answer is choice A.

Question 7

The mode of a symmetric, bell-shaped distribution should:

Accepted Answer

In a symmetric, bell-shaped distribution (often referred to as a normal distribution), the mean, median, and mode are all located at the center of the distribution and are equal to each other. This distribution is characterized by its unique mode, which coincides with the mean and median, hence all the given options are correct.

Question 8

What is the largest possible value of the sample standard deviation?

Accepted Answer

The sample standard deviation can theoretically increase indefinitely as the spread of the data increases, so there is no largest possible value.

Question 9

Marine was a black Labrador retriever that was trained to detect colorectal cancer by smelling the breath of patients with cancer.In one test to determine how well this dog could detect colorectal cancer, Marine correctly identified a bag containing the breath of a patient with colorectal cancer (from about five bags, with four containing the breath of healthy subjects) in 30 out of 33 trials.What is  (the sample proportion) in this situation?

Accepted Answer

The sample proportion represents the number of successful trials out of total trials. In this case, there were 33 total trials and Marine correctly identified the bag with the breath of a patient with colorectal cancer in 30 trials. Therefore, the sample proportion is:

Sample proportion = number of successful trials / total trials
Sample proportion = 30/33
Sample proportion = 0.91

Therefore, the answer is C, 0.91.

Question 10

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: ​
Xmin = 0, Q1 = 6,  = 15.5, Q3 = 24, xmax = 63,  = 18.92 = 18.92
​
Based on the five-number summary, the overall shape of the lengths of these reigns appears to be:

Accepted Answer

The minimum value is 0, which seems unlikely for a monarch's reign, indicating that there may be some outliers among the data. The median (Q2) is also closer to Q1 than to Q3, indicating that there are more low values than high values. Therefore, the data is skewed to the right.

Question 11

The median of the lower half of the observations when arranged in ascending order is the:

Accepted Answer

The first (lower) quartile is the point below which 25% of the observations in a data set fall when arranged in ascending order. The median of the lower half of the observations is another way of defining the first quartile. Therefore, choice C is the correct answer.

Question 12

The symbol  represents the:

Accepted Answer

The answer of The symbol  represents the:
...

Question 13

Calculate  for the following sample data set: ​  ​

Accepted Answer

The answer of Calculate  for the following sample data...

Question 14

If we have a distribution with ith deviation from the mean equal to 0, then we know that:

Accepted Answer

The ith deviation from the mean being 0 means that the ith observation is exactly equal to the mean, not affecting the symmetry, variance, or the relevance of the median.

Question 15

It is known that the body mass index (BMI) of healthy American males follows a normal distribution, with a mean of 24.5 and a standard deviation of 3.0.Approximately what proportion of male BMI values fall below 18.5?

Accepted Answer

To find the proportion of male BMI values below 18.5, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (18.5), μ is the mean (24.5), and σ is the standard deviation (3.0). Plugging in the values, we get Z = (18.5 - 24.5) / 3 = -6 / 3 = -2. A Z-score of -2 corresponds to approximately 2.5% of the distribution lying below this value, based on standard normal distribution tables.

Question 16

The smallest numeric value in a data set subtracted from the largest gives the:

Accepted Answer

The range is defined as the difference between the smallest and largest values in a data set. Therefore, the smallest numeric value subtracted from the largest gives the range.

Question 17

The __________ of a data set, if any, is the value that occurs most often, or with the greatest frequency.

Accepted Answer

The mode is the value that occurs most frequently in a data set. It is the best choice for determining the most common value in the data. The mean is the average value of the data set, which may not accurately represent the most common value if there are outliers in the data. The median is the middle value of a data set and may not necessarily represent the most common value. Relative frequency is a measure of how often an event occurs in relation to the total number of events. It is not appropriate for determining the mode of a data set.

Question 18

The _________ of a data set is the middle number when the observations are arranged in order from smallest to largest.

Accepted Answer

The definition given in the question is that of the median. The weighted mean is a type of mean which takes into account the weights of each observation. The mode is the most frequent value in the data set. The arithmetic mean is another type of mean which is found by summing all the observations and dividing by the total number of observations.

Question 19

If a set of data contains an odd number of values and the data are ordered from smallest to largest, then:

Accepted Answer

If the data set contains an odd number of values, there will be a single middle value. This middle value is known as the median. Therefore, the median is the single middle value.

Question 20

For any set of n numbers, the sum of all n deviations about the arithmetic mean will always be:

Accepted Answer

By definition, the arithmetic mean of a set of n numbers is the sum of the numbers divided by n. Therefore, the sum of all n deviations about the mean must be equal to zero. This is because some of the deviations will be positive and some will be negative, but they will all cancel each other out when added together.

Quiz 4: Numerical Summary Measures

Calculate for the following sample data set:

What is the smallest possible value for a sample standard deviation?

The following is an abbreviated list of scores from a recent exam.Which exam score is the 15th percentile?

The sample mean is:

Calculate s2 for the following sample data set:

The mode of a symmetric, bell-shaped distribution should:

What is the largest possible value of the sample standard deviation?

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: Xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63, = 18.92 = 18.92 Based on the five-number summary, the overall shape of the lengths of these reigns appears to be:

The median of the lower half of the observations when arranged in ascending order is the:

The symbol represents the:

Calculate for the following sample data set:

If we have a distribution with ith deviation from the mean equal to 0, then we know that:

It is known that the body mass index (BMI) of healthy American males follows a normal distribution, with a mean of 24.5 and a standard deviation of 3.0.Approximately what proportion of male BMI values fall below 18.5?

The smallest numeric value in a data set subtracted from the largest gives the:

The __________ of a data set, if any, is the value that occurs most often, or with the greatest frequency.

The _________ of a data set is the middle number when the observations are arranged in order from smallest to largest.

If a set of data contains an odd number of values and the data are ordered from smallest to largest, then:

For any set of n numbers, the sum of all n deviations about the arithmetic mean will always be:

Quiz 4: Numerical Summary Measures

Calculate for the following sample data set: ​ ​

What is the smallest possible value for a sample standard deviation?

The following is an abbreviated list of scores from a recent exam.Which exam score is the 15th percentile?

The sample mean is:

Calculate s2 for the following sample data set: ​ ​

The mode of a symmetric, bell-shaped distribution should:

What is the largest possible value of the sample standard deviation?

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: ​ Xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63, = 18.92 = 18.92 ​ Based on the five-number summary, the overall shape of the lengths of these reigns appears to be:

The median of the lower half of the observations when arranged in ascending order is the:

The symbol represents the:

Calculate for the following sample data set: ​ ​

If we have a distribution with ith deviation from the mean equal to 0, then we know that:

It is known that the body mass index (BMI) of healthy American males follows a normal distribution, with a mean of 24.5 and a standard deviation of 3.0.Approximately what proportion of male BMI values fall below 18.5?

The smallest numeric value in a data set subtracted from the largest gives the:

The __________ of a data set, if any, is the value that occurs most often, or with the greatest frequency.

The _________ of a data set is the middle number when the observations are arranged in order from smallest to largest.

If a set of data contains an odd number of values and the data are ordered from smallest to largest, then:

For any set of n numbers, the sum of all n deviations about the arithmetic mean will always be:

Calculate for the following sample data set:

Calculate s2 for the following sample data set:

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: Xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63, = 18.92 = 18.92 Based on the five-number summary, the overall shape of the lengths of these reigns appears to be:

Calculate for the following sample data set: