Question 1

Which measures of central location and variability are considered to be resistant to extreme values?
A) The mean and standard deviation.
B) The mode and variance.
C) The median and interquartile range.
D) None of these choices.

Accepted Answer

The median and interquartile range are resistant to extreme values, meaning that they are not greatly influenced by the presence of outliers. On the other hand, the mean and standard deviation are greatly affected by outliers and are not considered to be resistant measures of central location and variability. The mode and variance may or may not be influenced by outliers depending on the distribution of the data.

Question 2

Which of the following types of data has no measure of variability?
A) Interval data
B) Nominal data
C) Bimodal data
D) None of these choices.

Accepted Answer

Nominal data is categorical data where no quantitative measurements are taken. Therefore, there is no variability to measure. Interval data involves measurements on a scale with equal intervals between values, bimodal data refers to a distribution with two peaks, and none of the choices cannot be correct.

Question 3

The interquartile range is the difference between the: A) largest and smallest numbers in the data set. B) 25^th percentile and the 75^th percentile. C) median and the mean. D) None of these choices.

Accepted Answer

The interquartile range is defined as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. Option A describes the range, option C describes the difference between two other measures of central tendency, and option D is a general statement indicating none of the given options are correct.

Question 4

Another word for the mean of a data set is the ____________________.

Accepted Answer

The answer of Another word for the mean of a...

Question 5

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.75, this means that: A) there is very weak correlation B) the slope b₁ is = -0.75 C) the value of X is always greater than the value of Y D) None of these choices are true

Accepted Answer

When the coefficient of correlation (r) equals 0.75, it indicates a moderately strong positive linear correlation between X and Y. The slope of the regression line (b) can be calculated using the formula b = r*(Sy/Sx), where Sy and Sx are the standard deviations of Y and X, respectively. Therefore, if r is known and nonzero, the slope can be calculated. Option C is incorrect since we cannot assume that X is always greater than Y, and option A is incorrect since 0.75 indicates a moderate correlation, not a very weak one.

Question 6

The length of the box in the box plot portrays the:
A) median.
B) interquartile range.
C) range.
D) third quartile.

Accepted Answer

The length of the box in a box plot represents the interquartile range (IQR), which is the range between the first quartile (Q1) and third quartile (Q3).

Question 7

Which of the following is a property of r, the coefficient of correlation?
A) r always lies between 0 and 1.
B) r has no units.
C) If you switch the values of X and Y, the sign of r changes.
D) All of these choices are true.

Accepted Answer

The coefficient of correlation, denoted as r, is dimensionless, meaning it has no units. This is because it is a standardized measure of the strength and direction of the linear relationship between two variables. Options A and C are incorrect: r actually ranges between -1 and 1, and switching the values of X and Y does not change the sign of r, it remains the same because the correlation measures the strength and direction of a linear relationship irrespective of which variable is considered X or Y.

Question 8

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate?
A) Coefficient of variation and range
B) Mean and standard deviation
C) Interquartile range and median
D) Variance and interquartile range

Accepted Answer

Interquartile range and median are more appropriate when extreme values are present in the data as they are not influenced by outliers, unlike mean and standard deviation. The coefficient of variation and range may be affected by extreme values, and variance tends to be influenced heavily by outliers.

Question 9

Which of the following measures of variability is not sensitive to extreme values?
A) The range
B) The standard deviation
C) The interquartile range
D) The coefficient of variation

Accepted Answer

The interquartile range (IQR) is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1), making it based on the middle 50% of the data. Therefore, it is not affected by extreme values or outliers. However, the range is simply the difference between the highest and lowest value, so it is highly sensitive to extreme values. The standard deviation and coefficient of variation are also affected by extreme values, as they involve the calculation of squared deviations from the mean.

Question 10

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8?
A) The range equals 0.
B) The standard deviation equals 0.
C) The coefficient of variation equals 0.
D) All of these choices are true.

Accepted Answer

- The range is calculated by subtracting the smallest value from the largest value in the data set. In this case, the smallest and largest values are both 8, so the range is 0.
- The standard deviation is a measure of how spread out the data is from the mean. For this data set, all the values are the same, so each deviation from the mean is 0. This results in a standard deviation of 0 as well.
- The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage. Since the standard deviation is 0 and the mean is 8, any division by 8 will also result in 0. Therefore, the coefficient of variation is also 0.

Question 11

In a negatively skewed distribution, which of the following is the correct statement? A) The distance from Q₁ to Q₂ is smaller than the distance from Q₂ to Q₃ B) The distance from the smallest observation to Q₁ is larger than the distance from Q₃ to the largest observation C) The distance from the smallest observation to Q₂ is smaller than the distance from Q₂ to the largest observation D) The distance from Q₁ to Q₃ is twice the distance from the Q₁ to Q₂

Accepted Answer

In a negatively skewed distribution, the tail of the distribution is longer on the left side, indicating that there are more data points on the lower end of the distribution. Therefore, the smallest observation will be further away from the mode than the largest observation. This means that the distance from the smallest observation to Q₁ is larger than the distance from Q₃ to the largest observation.

Question 12

Which of the following summary measures cannot be easily approximated from a box plot?
A) The range
B) The interquartile range
C) The second quartile
D) The standard deviation

Accepted Answer

The standard deviation cannot be easily approximated from a box plot. It requires knowledge of the mean and individual data points. The other summary measures, such as the range, interquartile range, and second quartile, can be approximated or directly read off from a box plot.

Question 13

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be:
A) a large positive number.
B) a large negative number.
C) a positive or negative number close to zero.
D) None of these choices.

Accepted Answer

If two variables are unrelated, the covariance will be close to zero. This is because the covariance is a measure of the relationship between two variables and if there is no relationship, the covariance will be close to zero. A covariance of a large positive or negative number indicates a strong relationship between the variables, which is not the case when they are unrelated.

Question 14

Is a standard deviation of 10 a large number indicating great variability, or is it small number indicating little variability? To answer this question correctly, one should look carefully at the value of the:
A) mean.
B) standard deviation.
C) coefficient of variation.
D) mean dividing by the standard deviation.

Accepted Answer

The coefficient of variation (C) is the correct answer because it is a measure that indicates the extent of variability in relation to the mean of the population. It is calculated as the ratio of the standard deviation to the mean, and it provides a standardized measure of dispersion of a probability distribution or frequency distribution. This is useful for comparing the degree of variation from one data series to another, even if the means are drastically different from each other.

Question 15

Which of the following statements is true? A) The lower or first quartile is labeled Q₁ and is equal to the 25^th percentile. B) The second quartile is labeled Q₂ and is equal to the median. C) The upper or third quartile is labeled Q₃ and is equal to the 75^th percentile. D) All of these choices are true.

Accepted Answer

Each statement accurately describes quartiles: A) the first quartile is the 25th percentile, B) the second quartile is the median, and C) the third quartile is the 75th percentile.

Question 16

In a perfectly symmetric distribution, which of the following statements is false? A) The distance from Q₁ to Q₂ equals to the distance from Q₂ to Q₃ B) The distance from the smallest observation to Q₁ is the same as the distance from Q₃ to the largest observation C) The distance from the smallest observation to Q₂ is the same as the distance from Q₂ to the largest observation D) The distance from Q₁ to Q₃ is half of the distance from the smallest to the largest observation

Accepted Answer

In a perfectly symmetric distribution, the median (represented by Q₂) is also the midpoint of the distribution. Therefore, statement A is true. Additionally, statement B is true as the distance from the smallest observation to the median and the distance from the median to the largest observation must be equal in a symmetric distribution. Statement C is also true for the same reason. However, statement D is false. If the distribution is perfectly symmetric, then the distance from the smallest to largest observation would be split evenly on both sides of the median, making the distance from Q₁ to Q₃ equal to the distance from the smallest observation to the median plus the distance from the median to the largest observation. Therefore, the correct answer is D.

Question 17

The strength of the linear relationship between two interval variables can be measured by the:
A) coefficient of variation.
B) coefficient of correlation.
C) slope of the regression line.
D) Y-intercept.

Accepted Answer

The coefficient of correlation measures the strength and direction of the linear relationship between two interval variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship. The coefficient of variation (A) measures the variability of a single variable, while the slope of the regression line (C) measures the change in the dependent variable for a unit change in the independent variable. The Y-intercept (D) is the value of the dependent variable when the independent variable is equal to zero.

Question 18

The smaller the spread of scores around the mean:
A) the smaller the variance of the data set.
B) the smaller the standard deviation of the data set.
C) the smaller the coefficient of variation of the data set.
D) All of these choices are true.

Accepted Answer

All of these statements are true because the spread of scores around the mean directly affects the variance, standard deviation, and coefficient of variation of a data set. A smaller spread indicates that the data points are closer to the mean, leading to a smaller variance and standard deviation. Since the coefficient of variation is a standardized measure of dispersion that takes into account the mean of the dataset, a smaller spread around the mean also results in a smaller coefficient of variation.

Question 19

In a positively skewed distribution, which of the following is the correct statement? A) The distance from Q₁ to Q₂ is larger than the distance from Q₂ to Q₃ B) The distance from Q₁ to Q₂ is smaller than the distance from Q₂ to Q₃ C) The distance from Q₁ to Q₂ is twice the distance from Q₂ to Q₃ D) The distance from Q₁ to Q₂ is half the distance from Q₂ to Q₃.

Accepted Answer

In a positively skewed distribution, the tail of the distribution is on the right-hand side. This means that there are more extreme values on the right-hand side of the distribution. Therefore, the distance from Q₁ to Q₂, which is closer to the peak or median of the distribution, will be smaller than the distance from Q₂ to Q₃, which is farther away from the peak. Therefore, option B is the correct choice. The other options are not true for a positively skewed distribution.

Question 20

Which of the following are measures of the linear relationship between two variables?
A) The covariance
B) The coefficient of correlation
C) The variance
D) Both a and b

Accepted Answer

The covariance and coefficient of correlation are both measures of the linear relationship between two variables. The variance is not necessarily a measure of the linear relationship, as it can also describe the spread of a single variable. Therefore, the best choice is D, because both the covariance and coefficient of correlation are measures of the linear relationship between two variables.

Quiz 3: Numerical Descriptive Techniques

Which measures of central location and variability are considered to be resistant to extreme values?

Which of the following types of data has no measure of variability?

The interquartile range is the difference between the:

Another word for the mean of a data set is the ____________________.

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.75, this means that:

The length of the box in the box plot portrays the:

Which of the following is a property of r, the coefficient of correlation?

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate?

Which of the following measures of variability is not sensitive to extreme values?

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8?

In a negatively skewed distribution, which of the following is the correct statement?

Which of the following summary measures cannot be easily approximated from a box plot?

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern) , the covariance will be:

Is a standard deviation of 10 a large number indicating great variability, or is it small number indicating little variability? To answer this question correctly, one should look carefully at the value of the:

Which of the following statements is true?

In a perfectly symmetric distribution, which of the following statements is false?

The strength of the linear relationship between two interval variables can be measured by the:

The smaller the spread of scores around the mean:

In a positively skewed distribution, which of the following is the correct statement?

Which of the following are measures of the linear relationship between two variables?