Question 1

Which measure of central tendency is always present as an actual case value within a data set?&#10;A) the mode&#10;B) the median&#10;C) the mean&#10;D) the trimmed mean

Accepted Answer

The mode is the value that appears most frequently in the data set and is therefore always present as an actual case value within the data. The median and mean may not necessarily have an actual case value within the data set, especially if there are even numbers of observations or if there are extreme values that skew the distribution. The trimmed mean, which involves removing a specified percentage of extreme values from the data, also may not have an actual case value within the data set.

Question 2

In a social work course, an instructor wishes to assign a final grade based upon 10 percent for class discussion, 40 percent for a term paper, and 25 percent for each of two examinations. What measure of central tendency should she use in computing her final grades?

A) the mean
B) the median
C) the trimmed mean
D) the weighted mean

the weighted mean

Accepted Answer

The instructor is using different percentages for each component of the final grade, so a weighted mean (also known as a weighted average) is the most appropriate measure of central tendency to use in computing final grades. The weighted mean takes into account both the value of each component and its corresponding percentage weight.

Question 3

The statement that &#34;the largest number of assaults in our city were gang-related&#34; is another way of describing what statisticians refer to as the:&#10;A) mode.&#10;B) mean.&#10;C) variance.&#10;D) standard deviation.

Accepted Answer

The mode is the most frequently occurring value in a dataset. In this case, the statement is identifying the category (gang-related) that appears most frequently in the dataset of types of assault in the city.

Question 4

In a box plot, what do any numbered dots above or below the horizontal lines that are outside the box represent?&#10;A) the number of cases in the data set&#10;B) the case numbers of any outliers&#10;C) the frequency for the value that is the mode&#10;D) the range

Accepted Answer

Any numbered dots above or below the horizontal lines that are outside the box represent the case numbers of any outliers.

Question 5

A case value that is much larger or much smaller than most other values in a data set is called:&#10;A) a weighted mean.&#10;B) an outlier.&#10;C) a trimmed mean.&#10;D) a mode

Accepted Answer

A value that is much larger or much smaller than most other values in a data set is called an outlier. Outliers can greatly affect the measures of central tendency, such as the mean and the mode, and can skew the results of statistical analyses. Therefore, it is important to identify and handle outliers appropriately.

Question 6

An extremely large or small measurement of a variable has the greatest effect on the variable's&#10;A) median&#10;B) range&#10;C) inter-quartile range&#10;D) mode

Accepted Answer

The range is the difference between the highest and the lowest values in a dataset. If there is an extremely large or small measurement, it will increase the range significantly. The median and mode are measures of central tendency and are not as affected by outliers. The inter-quartile range only considers the middle 50% of the data and would not be as affected by extreme values.

Question 7

In a box plot, what does the horizontal line within the box represent? A) the trimmed mean B) the median C) the 25^th percentile rank D) the 75^th percentile rank

Accepted Answer

The horizontal line within the box represents the median, which is the middle value in the dataset when arranged in order.

Question 8

A measure of central tendency describes what was of a variable within a data set.&#10;A) the most unusual measurement&#10;B) the amount of variation in measurements&#10;C) a typical measurement&#10;D) the accuracy of measurements

Accepted Answer

A measure of central tendency, such as the mean or median, gives an idea of what a typical measurement is within a data set. It does not indicate the most unusual measurement (A), the amount of variation in measurements (B), or the accuracy of measurements (D).

Question 9

A measure of central tendency that is used to cancel out the effects of a few extremely large or small values of a variable within a data set is the:&#10;A) mode&#10;B) mean&#10;C) trimmed mean&#10;D) weighted mean

Accepted Answer

The trimmed mean is calculated by removing a certain percentage of the extreme values from the dataset, thereby reducing the impact of outliers on the overall measure of central tendency. This is a more robust measure than the mean, which is heavily influenced by extreme values, and is often preferred in situations where outliers are present. The mode is simply the most frequently occurring value, and the weighted mean gives more importance to certain values based on their weights.

Question 10

If an instructor adds five points to everyone's grade on an exam, what will not change?&#10;A) the mode&#10;B) the mean&#10;C) the median&#10;D) the standard deviation

Accepted Answer

Adding a constant to each data point increases the mean, median, and mode by that constant, but the standard deviation, which measures the spread of data, remains unchanged.

Question 11

What measure of variability uses only two case values in its computation?&#10;A) the range&#10;B) the inter-quartile range&#10;C) the mean deviation&#10;D) the variance

Accepted Answer

The answer of What measure of variability uses only two...

Question 12

In a distribution of a variable that can be described as &#34;bimodal,&#34;&#10;A) the mode, median, and mean all are about equal.&#10;B) the value with the highest frequency is twice as large as any other value.&#10;C) there are two values with about the same (the highest) frequencies.&#10;D) the mean is twice as large as the median.

Accepted Answer

The answer of In a distribution of a variable that...

Question 13

With what measure of variability do larger numbers represent more variation in the distribution of a variable?&#10;A) the range&#10;B) the inter-quartile range&#10;C) the standard deviation&#10;D) all of the above

Accepted Answer

The answer of With what measure of variability do larger...

Question 14

What measure of variability is the square root of the variance?&#10;A) the mean&#10;B) the mean deviation&#10;C) the standard deviation&#10;D) the inter-quartile range

Accepted Answer

The answer of What measure of variability is the square...

Question 15

Which measure of central tendency always falls at about the 50^th percentile rank? A) the mode B) the median C) the mean D) the weighted mean

Accepted Answer

The answer of Which measure of central tendency always falls...

Deck 3: Measures of Central Tendency and Variability