Question 1

The correlation coefficient cannot be greater than 1.0.

Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables, and its value ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and values outside this range are not possible.

Question 2

The interquartile range is used as a measure of variability to overcome what difficulty of the range?

Accepted Answer

The interquartile range is used as a measure of variability to overcome the issue that the range is influenced too much by extreme values, providing a more robust measure of spread that is less sensitive to outliers.

Question 3

The coefficient of variation is the preferred measure of dispersion when comparing the dispersion in data sets that have different means.

Accepted Answer

The coefficient of variation normalizes the standard deviation by the mean, making it a useful measure for comparing the relative variability between datasets with different units or scales.

Question 4

If a data value has a z-score of -2.75 then it is considered an outlier.

Accepted Answer

A z-score of -2.75 indicates the data value is 2.75 standard deviations below the mean, which is not typically considered an outlier unless the threshold is set at 2 or lower. Outliers are often identified with z-scores beyond ±3.

Question 5

The interquartile range is the difference between the 75 percentile and the 25 percentile values in a data set.

Accepted Answer

The interquartile range (IQR) is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3) in a data set, effectively measuring the spread of the middle 50% of the data.

Question 6

The correlation coefficient cannot be negative.

Accepted Answer

The correlation coefficient can be negative, indicating a negative or inverse relationship between two variables.

Question 7

The geometric mean is appropriate any time the values being averaged are of unequal importance.

Accepted Answer

The geometric mean is most appropriate for series that exhibit serial correlation—this typically involves rates of change and index numbers, not situations where values have unequal importance.

Question 8

Halston Communications (HC) hired 120 new workers last year.This put the company at the first quartile value among all firms in the greater Houston area.Explain what this means.

Accepted Answer

The answer of Halston Communications (HC) hired 120 new workers...

Question 9

When calculating the p^th percentile, if the index i is NOT an integer then take the average of the data values in the i - 1 and i + 1 positions.

Accepted Answer

When the index i is not an integer, you take the average of the data values at positions i (rounded down) and i+1 (the next position), not i-1 and i+1.

Question 10

Positive values of the covariance indicate a positive relation between the x and the y variables.

Accepted Answer

Covariance measures the direction of the relationship between two variables. A positive covariance indicates that as one variable increases, the other variable tends to increase as well, showing a positive relationship.

Question 11

In computing the p^th percentile, if the index i is NOT an integer the p^th percentile is the:

Accepted Answer

The answer of In computing the p^th percentile, if the...

Question 12

The empirical rule states that approximately 95.9% of values in a data set will be within two standard deviations of the mean if the data follows a bell-shaped curve.

Accepted Answer

The empirical rule states that approximately 95% of values in a data set will be within two standard deviations of the mean if the data follows a bell-shaped curve.

Question 13

The correlation coefficient is a standardized value that ranges between -1 and +1.

Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables, with -1 indicating a perfect negative linear correlation, +1 indicating a perfect positive linear correlation, and 0 indicating no linear correlation.

Question 14

The width of the box in a box-and-whisker plot is the interquartile range (IQR).

Accepted Answer

The width of the box in a box-and-whisker plot represents the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1), showing the middle 50% of the data.

Question 15

In computing the pth percentile, if the index i is NOT an integer, then round up to the next highest integer to get the pth percentile.

Accepted Answer

When the index i is not an integer, rounding up to the next highest integer ensures that the pth percentile corresponds to an actual data point in the ordered dataset.

Question 16

A stem-and-leaf display is a graph of a cumulative distribution.

Accepted Answer

A stem-and-leaf display is a graphical method of displaying quantitative data, not a graph of a cumulative distribution. It organizes data points based on their leading digits (the stem) and trailing digits (the leaf), allowing for a quick overview of the distribution of data, but it does not accumulate or sum the data as a cumulative distribution does.

Question 17

An outlier is a data value that has a z-score less than -1.5 or is greater than Q3-1.5*IQR.

Accepted Answer

An outlier is typically defined as a data value that is significantly different from other data points in a dataset. The common criteria for identifying outliers include having a z-score less than -3 or greater than 3, or being outside the range defined by Q1-1.5*IQR and Q3+1.5*IQR, where Q1 and Q3 are the first and third quartiles, respectively, and IQR is the interquartile range.

Question 18

The 50^th percentile of a data set:

Accepted Answer

The 50th percentile of a data set is the median. In a negatively skewed distribution, the mean is pulled towards the tail, which is on the left, making the mean smaller than the median. Therefore, the median (50th percentile) will tend to be larger than the mean if the distribution is negatively skewed.

Question 19

The interquartile range measures the middle 65% of the values in the data set.

Accepted Answer

The interquartile range measures the middle 50% of the values in a data set, covering the range between the first and third quartiles.

Question 20

The interquartile range is the difference between the third quartile and the first quartile values in the data set.

Accepted Answer

The interquartile range (IQR) measures the spread of the middle 50% of the data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

Quiz 3: Descriptive Statistics II: Additional Descriptive Measures and Data Displays