Question 1

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-the distribution of income scores is
A) skewed right
B) skewed left
C) skewed to the middle
D) not skewed

Accepted Answer

The mean is greater than the median, which suggests that there are some high-income outliers pulling the mean up and making the distribution skewed to the right. The mode being lower than the median and mean also supports this conclusion.

Question 2

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-the most appropriate measure of central tendency in this distribution Would yield a value of
A) $80,000
B) $100,000
C) $71,000
D) none of these values could yield a measure of central tendency

Accepted Answer

The median is the middle value when the data is sorted in order, and since it is given that the median is $80,000, it is a valid measure of central tendency. 
The mode, which is the most common value, is often not a good measure of central tendency for skewed distributions such as this one. 
The mean, which is the sum of all values divided by the number of values, is affected by outliers and can be distorted in skewed distributions, as it is in this case ($100,000 is higher than the median and influenced by higher earners). Therefore, the best choice among the options is the median, as it is not influenced by extreme values.

Question 3

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-The annual income which is surpassed by 90% of the families is
A) $100,000
B) $71,000
C) $80,000
D) cannot tell from these data

Accepted Answer

The information provided (median, mean, and mode) does not give specific details about the distribution of income across percentiles, such as the income surpassed by 90% of the families. Therefore, we cannot determine this value from the given data.

Question 4

In a histogram, the mode is always located
A) under the shortest bar
B) under the tallest bar
C) under the last bar to the right
D) under the last bar to the left

Accepted Answer

The mode in a histogram is the value that appears most frequently in the data set. It is represented by the tallest bar in the histogram because it has the highest frequency. Therefore, the mode is always located under the tallest bar in the histogram.

Question 5

Whenever a distribution is skewed left, the measure yielding the highest numerical value is always the
A) mean
B) median
C) mode
D) percentile

Accepted Answer

In a left-skewed distribution, the mode is the highest value among the mean, median, and mode because it represents the peak of the distribution, which is on the right side of the skew. The mean is pulled toward the tail, and the median is between the mean and mode, making the mode the highest.

Question 6

When a skewed distribution tails off to the right, the distribution is
A) skewed right
B) skewed left
C) skewed to the center
D) not skewed at all

Accepted Answer

A skewed distribution with a tail off to the right is called skewed right. The majority of the data points will be on the left side of the graph, with a few outliers extending the tails to the right.

Question 7

When the median lies to the right of the mean, the distribution is probably
A) bimodal
B) multimodal
C) skewed left
D) skewed right

Accepted Answer

If the median lies to the right of the mean, it means that there are some larger values on the right tail pulling the median to the right. This indicates that the distribution is skewed left.

Question 8

Adding just one or two extreme scores to the high end of a distribution, has a great effect on
A) the median, but not the mode
B) the mode, but not the mean
C) the mean, but not the median
D) none of these

Accepted Answer

Adding extreme scores to the high end of a distribution will increase the sum of the values and the number of values included in the calculation of the mean. This will greatly impact the mean but not the median. The mode may or may not be affected depending on the specific values added.

Question 9

When the majority of scores are at the high end of the distribution, but there are a few extremely low scores, the distribution is
A) bimodal
B) multimodal
C) skewed left
D) skewed right

Accepted Answer

A distribution in which the majority of the scores are at the high end, but there are a few extremely low scores is a left-skewed distribution.

Question 10

Adding just one or two extreme scores to the low end of a distribution, has a great effect on
A) the median but not the mode
B) the mode, but not the median
C) the mean, but not the median
D) none of these

Accepted Answer

The mean is heavily affected by extreme scores, but the median and mode are more resistant to outliers on the low end of a distribution.

Question 11

Bar charts are used instead of histograms when the data are
A) Continuous
B) Non-continuous
C) In the form of values that may fall at any point along an unseparated scale of points
D) None of these since bar charts and histograms are synonymous.

Accepted Answer

Bar charts are used for non-continuous data, while histograms are used for continuous data. Non-continuous data can be categorical, such as types of food or colors, and cannot be measured on a continuous scale.

Question 12

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-the annual income achieved by most of the families is
A) $71,000
B) $80,000
C) $100,000
D) half way between the mean and the mode

Accepted Answer

The mode is defined as the value that appears most frequently in the dataset. Therefore, $71,000 is the value that occurs most frequently in this community. 
The median is the middle value when the dataset is arranged in increasing order. Since the median income is $80,000, it means that half of the families make more than $80,000 and half make less. 
The mean is the sum of all values divided by the number of values. In this case, the mean income is $100,000. The fact that the mean income is larger than the median income suggests that there are some families earning much more than the others, pulling the mean up.

Based on this information, we can conclude that the income achieved by most families in this community is $71,000, which is the mode.

Question 13

The most frequently occurring score in the distribution defines the
A) mean
B) median
C) sigma
D) mode

Accepted Answer

The mode is the score that occurs most frequently in the distribution, so it is the best choice for this question. The mean and sigma are measures of central tendency and variability, respectively, but they do not necessarily reflect the most frequently occurring score in the distribution. The median is the middle score in the distribution, so it may or may not be the same as the mode.

Question 14

The point above which half the scores fall and below which half the scores fall, defines the
A) mean
B) median
C) sigma
D) mode

Accepted Answer

The point above which half the scores fall and below which half the scores fall is the definition of the median.

Question 15

The mean is not overly affected by extreme scores, unless
A) the extreme scores are all in one direction
B) the extreme scores are in both directions
C) the number of extreme scores is fewer than 5
D) all of these

Accepted Answer

The mean is sensitive to extreme scores if they are all in one direction, meaning they are either all very high or very low. If the extreme scores are in both directions, they can sometimes cancel each other out and not have as big of an impact on the mean. If the number of extreme scores is fewer than 5, it may or may not have a significant effect depending on the size of the data set. Therefore, choice A is the best answer as it accurately describes the situation where the mean is most affected by extreme scores.

Question 16

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-The annual income which is surpassed by 50% of the families is
A) $80,000
B) $71,000
C) $100,000
D) cannot tell from these data

Accepted Answer

The median income is $80,000, which means that 50% of the families make above $80,000 and 50% make below. Therefore, the annual income which is surpassed by 50% of the families is $80,000.

Question 17

In a certain community, the median per-family annual income is $80,000.  The 
Mean per-family income is $100,000, whereas the mode is $71,000.
-if a new family were to move into the community with an annual income of $295,000, this would most affect
A) the mean
B) the median
C) the mode
D) all of these

Accepted Answer

The mean is the average, which is affected by extreme values. Adding a family with an income of $295,000 would significantly increase the total income and therefore increase the mean per-family income, without affecting the median or mode.

Question 18

The arithmetic average defines the
A) mean
B) median
C) sigma
D) mode

Accepted Answer

The arithmetic average is also known as the mean, which is the sum of all values in a dataset divided by the number of values in the dataset. It is a measure of the central tendency of the data. The median is the middle value in a dataset, while the mode is the value that appears most frequently. Sigma is a symbol used to represent standard deviation, which is a measure of the spread or variability of the data.

Question 19

The fact that the mean IQ of college seniors is higher than that of freshmen is probably due to
A) the fact that going to college increases the IQ
B) the fact that there is a big IQ gain between the junior and senior years
C) an incorrect interpretation of the data
D) the fact that the lower IQ freshmen tend to drop out of college and,

Accepted Answer

Many students with lower IQ scores may not make it to their senior year because they drop out of college. This leaves behind a higher concentration of students with higher IQ scores, which skews the data towards a higher mean IQ among college seniors.

Question 20

When the mean lies to the right of the median, the distribution is probably
A) bimodal
B) multimodal
C) skewed left
D) skewed right

Accepted Answer

If the mean is greater than the median, it suggests that there are some outliers on the higher end, pulling the mean towards the right. This results in a long tail on the right side of the distribution, indicating a right skew.

Quiz 2: Percentages, Graphs and Measures of Central Tendency

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -the distribution of income scores is

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -the most appropriate measure of central tendency in this distribution Would yield a value of

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -The annual income which is surpassed by 90% of the families is

In a histogram, the mode is always located

Whenever a distribution is skewed left, the measure yielding the highest numerical value is always the

When a skewed distribution tails off to the right, the distribution is

When the median lies to the right of the mean, the distribution is probably

Adding just one or two extreme scores to the high end of a distribution, has a great effect on

When the majority of scores are at the high end of the distribution, but there are a few extremely low scores, the distribution is

Adding just one or two extreme scores to the low end of a distribution, has a great effect on

Bar charts are used instead of histograms when the data are

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -the annual income achieved by most of the families is

The most frequently occurring score in the distribution defines the

The point above which half the scores fall and below which half the scores fall, defines the

The mean is not overly affected by extreme scores, unless

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -The annual income which is surpassed by 50% of the families is

In a certain community, the median per-family annual income is $80,000. The Mean per-family income is $100,000, whereas the mode is $71,000. -if a new family were to move into the community with an annual income of $295,000, this would most affect

The arithmetic average defines the

The fact that the mean IQ of college seniors is higher than that of freshmen is probably due to

When the mean lies to the right of the median, the distribution is probably