Question 1

A skewed distribution tends to pull the median,but not the mean,toward outliers in the data.

Accepted Answer

A skewed distribution tends to pull the mean toward the outliers, not the median. The median remains more centrally located and is less affected by outliers.

Question 2

The mode is always the middle score in a distribution.

Accepted Answer

The mode is not necessarily the middle score in a distribution. It is the score that occurs most frequently in a data set. In some cases, there may be multiple modes or no mode at all.

Question 3

The weighted mean is used to determine the mean for samples with unequal sample sizes.

Accepted Answer

The weighted mean is calculated by multiplying each value in the sample by a weight that represents its importance or frequency. This is particularly useful when dealing with samples of unequal size, as it takes into account each value's influence on the overall mean.

Question 4

A researcher measures the following scores on an assessment: 2,3,7,3,5,6,and 9.In this example,the mean is smaller than the median.

Accepted Answer

The mean is calculated by adding up all the scores and dividing by the total number of scores. In this case, (2+3+7+3+5+6+9) / 7 = 5. The median is the middle score when the scores are arranged in order. In this case, the scores arranged in order are: 2,3,3,5,6,7,9. The middle score is 5. Therefore, the mean is not smaller than the median.

Question 5

A weighted mean should be used when the "weights" are not equal.

Accepted Answer

A weighted mean takes into account the importance or significance of each data value. The weights represent how much each data value contributes to the overall mean. If the weights are not equal, a weighted mean should be used instead of a simple arithmetic mean.

Question 6

Adding a new score to a set of scores will change the mean,even when the score that is added is equal to the mean.

Accepted Answer

Adding a score that is equal to the current mean will not change the mean, as the total sum increases by the mean value and the count of numbers increases by one, keeping the mean unchanged.

Question 7

The mode and the median are always the same value.

Accepted Answer

The mode is the value that appears most frequently in a set of data, while the median is the middle value when the data is arranged in order. These two values may or may not be the same, depending on the distribution of the data. For example, in a set of data with a single mode (one value appearing more frequently than any other), the mode and median may be the same. However, in a set of data with multiple modes or a skewed distribution, the mode and median are likely to be different values.

Question 8

A researcher measures the depth (in fathoms)of different points in the ocean affected most by pollution.Based on the scale of measurement for these data,describing the mean depth is appropriate.

Accepted Answer

Since the scale of measurement is quantitative (measured in fathoms), the mean can be used as an appropriate measure of central tendency to describe the average depth of the polluted points in the ocean.

Question 9

A weighted mean weighs the mean by the sample size for each sample in the formula.

Accepted Answer

A weighted mean takes into account the sample size for each sample, giving more weight to samples with a larger size, thus the mean is weighted.

Question 10

A weighted mean is most appropriate to describe the mean for two or more samples with equal sample sizes.

Accepted Answer

A weighted mean is most appropriate when combining means from different samples that have unequal sizes or when the data points have different levels of importance.

Question 11

Some,but not all,scores in a distribution are included in the calculation of a mean.

Accepted Answer

The mean is calculated by summing all the scores in a distribution and then dividing by the total number of scores, thus including all scores.

Question 12

The median cannot be at the center of a distribution if the mean is also at the center of the distribution.

Accepted Answer

This statement is false. It is possible for the median and mean to both be at the center of a distribution. This would occur if the distribution is symmetrical, such as a normal distribution. In this case, the median and mean would both be located at the peak or center of the curve.

Question 13

The mean,median,and mode are all the same value in a normal distribution.

Accepted Answer

The mean, median, and mode are all the same in a perfectly symmetrical normal distribution.

Question 14

It is appropriate to use the mode with the mean to describe data that are skewed.

Accepted Answer

It is not appropriate to use the mode with the mean to describe skewed data as the mode may not represent the central tendency of the data. In such cases, it is better to use the median as a measure of central tendency.

Question 15

The mode can be used to describe modal distributions.

Accepted Answer

The mode is a measure of central tendency that represents the most frequently occurring value in a distribution. When a dataset has a modal distribution (meaning it has one prominent peak), the mode can be used to describe the location of that peak.

Question 16

The sum of the squared differences of scores from their mean is zero.

Accepted Answer

The sum of the squared differences of scores from their mean is not zero; it is a positive value unless all scores are identical to the mean, in which case the differences would be zero, but this is a specific condition, not the general rule. This sum is used in calculating variance, a measure of dispersion in a dataset.

Question 17

The sum of the differences of scores from their mean is zero.

Accepted Answer

This is a property of the mean in statistics. This means that for any set of scores (or data points), if you take the difference of each score from their mean, and add up all those differences, the result will be zero.

Question 18

A researcher measures the following scores on a quiz: 0,3,7,3,5,4,and 6.In this example,the mean is larger than the median.

Accepted Answer

The mean is 4 (28 divided by 7), and the median is 4 (when the scores are ordered, the middle score is 4), so the mean is not larger than the median; they are equal.

Question 19

A researcher records the distance (in feet)traveled in a burning building by firefighters during a rescue attempt.Based on the scale of measurement for these data,describing the mean distance traveled is appropriate.

Accepted Answer

Since the distance traveled is a continuous variable that has a meaningful zero, it is appropriate to use the mean as a measure of central tendency.

Question 20

It is possible to compute a sample mean that is larger than the value of the actual population mean.

Accepted Answer

This is possible if the sample is not a representative of the whole population or there are outliers in the sample data that affect the mean.

Quiz 3: Summarizing Data: Central Tendency