1.
Which of the following statements about the median is NOT true?
Correct Answer
B. The median is more affected by extreme values than the mean.
Explanation
The statement "The median is more affected by extreme values than the mean" is NOT true. The median is less affected by extreme values because it only considers the middle value(s) in a data set, while the mean takes into account all values. Extreme values can greatly influence the mean, but they have less impact on the median.
2.
It is possible that a distribution of data may not actually contain one of the measures of central tendency. Which one might that be?
Correct Answer
A. The Mode
Explanation
In a distribution of data, it is possible that there may not be a mode, which is the value that appears most frequently. This can occur when all values in the data set occur with equal frequency or when there is no value that occurs more than once. Therefore, the correct answer is the Mode.
3.
As a general rule, a data point is considered to be an outlier if it is
Correct Answer
A. More than three standard deviations away from the mean
Explanation
An outlier is a data point that is significantly different from the other data points in a dataset. In statistics, it is commonly defined as a data point that is more than three standard deviations away from the mean. This means that the data point is located in the tails of the distribution and is considered to be an extreme value. By setting the threshold at three standard deviations, it ensures that only extreme values are classified as outliers, rather than including data points that may be slightly different but still within a reasonable range.
4.
In a right-skewed distribution:
Correct Answer
D. The mean is greater than the median.
Explanation
In a right-skewed distribution, the tail of the distribution is longer on the right side, indicating that there are a few extremely high values that pull the mean towards the right. Since the mean is affected by extreme values, it is greater than the median, which represents the middle value of the distribution. Therefore, the mean is greater than the median in a right-skewed distribution.
5.
Applicants to MBA programs typically must submit graduate-level board scores known as the GMAT. Assuming that the distribution of GMAT scores is symmetrical and bell shaped, then fifty-percent of all scores would be greater than which value?
Correct Answer
E. All of the above
Explanation
Since the distribution of GMAT scores is assumed to be symmetrical and bell-shaped, the mean, median, and mode would all be equal. Therefore, if fifty percent of all scores are greater than the mean, then fifty percent of all scores would also be greater than the median and the mode. Thus, the correct answer is "all of the above".
6.
A survey question which asks whether or not the respondent is “for” or “against” a proposal represents
Correct Answer
C. A categorical variable.
Explanation
A survey question asking whether the respondent is "for" or "against" a proposal represents a categorical variable because it classifies the respondents into distinct categories or groups based on their stance. The variable does not have a numerical value or a range of values, but rather represents different options or choices.
7.
The branch of statistics that uses sample data to draw conclusions about an entire population is known as:
Correct Answer
D. Inferential statistics
Explanation
Inferential statistics is the correct answer because it refers to the branch of statistics that uses sample data to make inferences or draw conclusions about a larger population. It involves analyzing and interpreting the data collected from a sample and using that information to make predictions or generalizations about the entire population. This is different from descriptive statistics, which focuses on summarizing and describing the characteristics of a sample or population. Experimentation and primary sources are not directly related to the process of drawing conclusions from sample data.
8.
Responses to survey question number one, “How many days did it take from the time you ordered your merchandise to the time you received it?” represents what kind of variable?
Correct Answer
B. Discrete and numerical
Explanation
The answer is "Discrete and numerical" because the question asks for a specific number of days, which is a discrete variable since it can only take on whole number values. Additionally, it is a numerical variable because it represents a quantity or measurement.
9.
What type of distribution is observed when most of the scores cluster around the lower end of the scale?
Correct Answer
C. A positively skewed distribution
Explanation
A positively skewed distribution is observed when most of the scores cluster around the lower end of the scale. This means that the majority of the data points are located towards the left side of the distribution, with a long tail extending towards the right. In this type of distribution, the mean is typically higher than the median, indicating that there are a few extremely high scores that pull the mean in that direction.
10.
Which two measures use the mean as a baseline and identify the extent to which scores differ from this?
Correct Answer
A. Variance and standard deviation
Explanation
Variance and standard deviation both use the mean as a baseline and measure the extent to which scores differ from it. Variance calculates the average squared deviation from the mean, providing a measure of the spread of data points. Standard deviation is the square root of variance and represents the average distance between each data point and the mean. Therefore, variance and standard deviation are the two measures that fulfill the requirement mentioned in the question.
11.
A tire manufacturer found a sample of tires created using a new formulation resulted in an average of forty-thousand miles per tire, and concluded that they can safely advertise this finding about the entire population of tires created with the new formula. This decision making process represents the branch of statistics known as descriptive statistics.
Correct Answer
B. False
Explanation
The given statement is false. The decision-making process described in the question represents the branch of statistics known as inferential statistics, not descriptive statistics. Descriptive statistics involves summarizing and describing data, while inferential statistics involves making inferences and predictions about a population based on a sample. In this case, the tire manufacturer is making an inference about the entire population of tires based on a sample, which falls under the realm of inferential statistics.
12.
A business student applying to an MBA program must complete a standardized exam known as the GMAT, which is measured on an interval scale.
Correct Answer
A. True
Explanation
The statement is true because the GMAT is indeed measured on an interval scale. This means that the scores on the GMAT have equal intervals between them, allowing for meaningful comparisons and calculations. The interval scale is commonly used in standardized tests to provide a more precise measurement of a student's abilities and skills.
13.
One of the advantages of a bar chart is that it clearly shows that the total of all the categories of the bar chart adds to 100%
Correct Answer
B. False
Explanation
A bar chart does not necessarily show that the total of all the categories adds to 100%. A bar chart is a visual representation of data using rectangular bars, where the length of each bar corresponds to the value it represents. The height of the bars may vary depending on the scale used. The total of all the categories can be any value and does not have to add up to 100%. Therefore, the statement is false.
14.
The coefficient of variation (CV) measures the variability in a data set relative to the size of the median.
Correct Answer
B. False
Explanation
The coefficient of variation (CV) actually measures the variability in a data set relative to the size of the mean, not the median. The CV is calculated by dividing the standard deviation of the data set by the mean, and it is often used to compare the variability of different data sets with different means. Therefore, the statement that the CV measures the variability relative to the size of the median is incorrect.
15.
The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 3.4
Correct Answer
B. False
Explanation
The median is the middle value of a set of numbers when they are arranged in ascending or descending order. In this case, the values are already in ascending order: 1.9, 3.4, 4.7, 6.5, 7.6. The middle value is 4.7, not 3.4. Therefore, the correct answer is False.