Question 1

When new scores that are close to the mean are added to any distribution, there is a fairly high probability that the range will
A) remain unaffected
B) be reduced
C) be increased
D) new scores may never be added to a distribution

Accepted Answer

Adding new scores that are close to the mean will not significantly affect the distribution's range, as the range is determined by the difference between the highest and lowest scores in the distribution, which are not likely to be affected by the addition of scores near the mean.

Question 2

If 50% of the cases fall above a given point, then 50% must also fall
A) below that point
B) between the mean and median
C) between the first and fifth deciles
D) none of these, since the distribution can never account for 100% of the

Accepted Answer

If 50% of the cases fall above a given point, then by definition, the remaining 50% must fall below that point.

Question 3

Of the following, which can be calculated even though the data are in ordinal form?
A) interquartile range
B) interdecile range
C) the middle-most 50% of the scores
D) all of these

Accepted Answer

Ordinal data allows for the ranking of items, making it possible to calculate measures of spread that involve ordering but not the actual values of the data. This includes the interquartile range, interdecile range, and identifying the middle-most 50% of scores, as all these measures depend on the order of data rather than their specific values.

Question 4

One major defect of the range is that
A) it includes the entire width of the distribution
B) it is based on only two scores
C) it is not a measure of variability
D) all of these

Accepted Answer

The range is based on only two scores and does not take into account the variability between all the other scores in the distribution. While it does include the entire width of the distribution, it is not a comprehensive measure of variability. Therefore, option A is incorrect. Option C is also incorrect, as the range is a measure of variability, but it has limitations due to its reliance on only the two extreme scores.

Question 5

The standard deviation is a measure of
A) how far all the scores vary from the mean
B) how far the middle-most 50% of cases vary from the mean
C) how far the highest and lowest scores vary from each other
D) central tendency

Accepted Answer

The standard deviation measures how much each score varies from the mean, indicating the spread of the data. Option B describes the interquartile range, option C describes the range, and option D describes measures of central tendency such as the mean or median.

Question 6

The third quartile begins between the
A) 1st and 5th deciles
B) 2nd and 3rd deciles
C) 4th and 6th deciles
D) 7th and 8th deciles

Accepted Answer

The third quartile (Q3) represents the 75th percentile, which falls between the 7th (70th percentile) and 8th (80th percentile) deciles.

Question 7

Specific points may be located on any distribution by using the
A) percentile
B) quartile
C) decile
D) all of these

Accepted Answer

All of these options can be used to locate specific points on a distribution.

Percentiles divide the data into 100 equal parts, with each part representing 1% of the data. For example, the 80th percentile represents the point below which 80% of the data lies.

Quartiles divide the data into four equal parts, with each part representing 25% of the data. The first quartile (Q1) represents the point below which 25% of the data lies, the second quartile (Q2) represents the median or middle point of the data, and the third quartile (Q3) represents the point below which 75% of the data lies.

Deciles divide the data into ten equal parts, with each part representing 10% of the data. For example, the 5th decile represents the point below which 50% of the data lies.

Question 8

Of the following, which should not be calculated when the data are in ordinal form?
A) median
B) quartile
C) decile
D) mean

Accepted Answer

The mean requires interval or ratio data, where the distance between each value is equal. In ordinal data, the values have a specific order but the intervals between them may not be equal. Therefore, the mean is not an appropriate measure of central tendency for ordinal data. The median, quartile, and decile are all appropriate measures of central tendency for ordinal data.

Question 9

A score which is at the 95th percentile must exceed
A) at least 5% of the scores
B) at least 95% of the scores
C) at least 45% of the scores
D) at least the lowest 47.50% of the scores

Accepted Answer

The 95th percentile corresponds to the score that is greater than 95% of the scores. Therefore, the correct answer is B.

Question 10

When a student takes a 600-item standardized test and is told he/she is at the 70th percentile, it means that the student
A) answered 30% of the items correctly
B) answered more than 70% of the items correctly
C) answered exactly 420 items correctly
D) none of these

Accepted Answer

The 70th percentile means that the student scored higher than 70% of the students who took the test, but it does not tell us how many items were answered correctly.

Question 11

The concept of "individual differences" may best be described by
A) the mode
B) the median
C) the measures of central tendency
D) the measures of variability

Accepted Answer

Individual differences refer to the variations among individuals in a population or sample. Measures of variability, such as standard deviation or range, are used to quantify these differences. Therefore, the best choice to describe individual differences is D - the measures of variability.

Question 12

A score which falls at the 50th percentile must always be at the
A) mean
B) mode
C) median
D) none of these

Accepted Answer

The 50th percentile always refers to the median, which is the value that divides the data into two equal parts. Therefore, a score at the 50th percentile must always be at the median.

Question 13

The fifth decile coincides with the
A) 50th percentile
B) 2nd quartile
C) median
D) all of these

Accepted Answer

The fifth decile, 50th percentile, 2nd quartile, and median all refer to the same point in a data set, which is the value below which 50% of the data falls.

Question 14

The difference between the highest and lowest scores in any distribution is called
A) the deviation score
B) the standard deviation
C) the range
D) none of these

Accepted Answer

The range is the difference between the highest and lowest scores in any distribution, whereas the deviation score and standard deviation refer to measures of variability around the mean.

Question 15

The first quartile coincides with the
A) first percentile
B) twenty-fifth percentile
C) seventy-fifth percentile
D) median

Accepted Answer

The first quartile (Q1) is equivalent to the 25th percentile, meaning that 25% of the data falls below this value. Therefore, the correct choice is option B. The first percentile is a much lower value and corresponds to the lowest 1% of the data, while the median is the middle value and corresponds to the 50th percentile. The 75th percentile is the third quartile (Q3).

Question 16

The interdecile range lies between the
A) 3rd and 7th deciles
B) 2nd and 8th deciles
C) 1st and 9th deciles
D) median and the 10th decile

Accepted Answer

The interdecile range is the range between the 1st decile (10th percentile) and the 9th decile (90th percentile), covering the middle 80% of the data distribution.

Question 17

The interquartile range lies between
A) the median and the third quartile
B) the median and the first quartile
C) the median and the lowest score in the distribution
D) the first and third quartiles

Accepted Answer

The interquartile range is defined as the difference between the first quartile and third quartile. Therefore, it lies between the first and third quartiles (choice D).

Question 18

The measure of the entire width of the distribution is called the
A) range
B) percentile
C) quartile
D) b and c, but not a

Accepted Answer

The measure of the entire width of the distribution is called the range. Percentile and quartile are measures of position in a distribution, not measures of its width.

Question 19

Of the following, the measure(s) of variability is (are),
A) the range
B) the standard deviation
C) the mode
D) a and b, but not c

Accepted Answer

The range and standard deviation are both measures of variability as they both provide information about the spread of the data. The mode, on the other hand, is a measure of central tendency and does not provide information about the variability. Therefore, the best choice is a and b, but not c.

Question 20

The interquartile range includes the middle-most
A) 25% of the cases
B) 50% of the cases
C) 75% of the cases
D) 95% of the cases

Accepted Answer

The interquartile range (IQR) represents the range of the middle 50% of the cases, which includes the 25th to the 75th percentile. Therefore, the correct choice is B, which states that the IQR includes 50% of the cases. Choices A, C, and D are incorrect because they either underestimate or overestimate the range of cases included in the IQR.

Quiz 3: Measures of Variability

When new scores that are close to the mean are added to any distribution, there is a fairly high probability that the range will

If 50% of the cases fall above a given point, then 50% must also fall

Of the following, which can be calculated even though the data are in ordinal form?

One major defect of the range is that

The standard deviation is a measure of

The third quartile begins between the

Specific points may be located on any distribution by using the

Of the following, which should not be calculated when the data are in ordinal form?

A score which is at the 95th percentile must exceed

When a student takes a 600-item standardized test and is told he/she is at the 70th percentile, it means that the student

The concept of "individual differences" may best be described by

A score which falls at the 50th percentile must always be at the

The fifth decile coincides with the

The difference between the highest and lowest scores in any distribution is called

The first quartile coincides with the

The interdecile range lies between the

The interquartile range lies between

The measure of the entire width of the distribution is called the

Of the following, the measure(s) of variability is (are) ,

The interquartile range includes the middle-most