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Unit 3: Measures of Central Tendency and variability - Practice Quiz

PSY115 — Statistical Methods For Psychological Research 60 Questions
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1 What is the median of the scores 3, 5, 7, 9, and 11?

the median Easy
A. 7
B. 9
C. 8
D. 5

2 What is the median of the scores 4, 6, 8, and 10?

the median Easy
A. 6
B. 8
C. 7
D. 9

3 What is the mode of the scores 2, 4, 4, 5, and 7?

the mode Easy
A. 5
B. 4
C. 2
D. 7

4 Which measure of central tendency identifies the most frequently occurring score?

the mode Easy
A. Mean
B. Range
C. Median
D. Mode

5 What is the arithmetic mean of 4, 6, and 8?

the mean Easy
A. 8
B. 5
C. 7
D. 6

6 Which formula represents the mean of a set of scores?

the mean Easy
A. Most frequent score
B. Sum of scores divided by number of scores
C. Largest score minus smallest score
D. Middle score in an ordered set

7 If every score in a data set is increased by 5, what happens to the mean?

the mean Easy
A. It increases by 5
B. It stays the same
C. It decreases by 5
D. It becomes zero

8 What is the range of the scores 6, 9, 12, and 15?

range Easy
A. 8
B. 21
C. 9
D. 6

9 Which expression is used to calculate the range?

range Easy
A. Largest value minus smallest value
B. Sum divided by the number of values
C. Smallest value plus largest value
D. Upper quartile minus median

10 A data set has a minimum value of 12 and a maximum value of 30. What is its range?

range Easy
A. 42
B. 18
C. 12
D. 30

11 What does the interquartile range measure?

interquartile and the semi-interquartile range Easy
A. The total number of scores
B. The most common score
C. The spread of the middle 50% of scores
D. The average of all scores

12 If the first quartile is 10 and the third quartile is 18, what is the interquartile range?

interquartile and the semi-interquartile range Easy
A. 4
B. 28
C. 8
D. 10

13 What is the semi-interquartile range?

interquartile and the semi-interquartile range Easy
A. The interquartile range multiplied by 2
B. The interquartile range divided by 2
C. The range divided by 2
D. The mean divided by 2

14 If the interquartile range is 14, what is the semi-interquartile range?

interquartile and the semi-interquartile range Easy
A. 28
B. 7
C. 5
D. 14

15 What does the average deviation describe?

the average deviation Easy
A. The most frequent score in a set
B. The average distance of scores from a central value
C. The difference between the largest and smallest scores
D. The product of all scores

16 When calculating average deviation from the mean, which type of deviations is used?

the average deviation Easy
A. Squared scores only
B. Ranked deviations
C. Absolute deviations
D. Signed deviations

17 What does standard deviation measure?

the standard deviation and variance Easy
A. The middle score in a data set
B. The total number of scores
C. The most frequent score
D. The typical spread of scores around the mean

18 What is the relationship between variance and standard deviation?

the standard deviation and variance Easy
A. Variance is standard deviation plus one
B. Variance is unrelated to standard deviation
C. Variance is the square of standard deviation
D. Variance is half of standard deviation

19 If the variance of a data set is 25, what is its standard deviation?

the standard deviation and variance Easy
A. 10
B. 5
C. 20
D. 625

20 If all scores in a data set are identical, what is their standard deviation?

the standard deviation and variance Easy
A. The largest score
B. 1
C. The mean
D. 0

21 A researcher records the reaction times, in seconds, as and . What is the median reaction time?

the median Medium
A. seconds
B. seconds
C. seconds
D. seconds

22 A data set has observations with a median of . If the largest observation is increased substantially, what happens to the median?

the median Medium
A. It decreases slightly
B. It remains
C. It becomes the new maximum
D. It increases substantially

23 The numbers of errors made by participants are and . What is the mode?

the mode Medium
A.
B.
C.
D.

24 A distribution of preferred therapy formats has frequencies: online , individual , group , and telephone . Which measure is most directly represented by the category with frequency ?

the mode Medium
A. The mean preference
B. The median preference
C. The modal preference
D. The range of preferences

25 The mean score of participants is . Five scores are and . What is the sixth score?

the mean Medium
A.
B.
C.
D.

26 A researcher adds points to every score in a test data set. If the original mean was , what is the new mean?

the mean Medium
A.
B.
C.
D.

27 Two groups have means of and , with and participants respectively. What is the combined mean?

the mean Medium
A.
B.
C.
D.

28 The observed stress scores are and . What is the range?

range Medium
A.
B.
C.
D.

29 A data set has a minimum value of and a range of . What is its maximum value?

range Medium
A.
B.
C.
D.

30 Which change leaves the range unchanged for the data set ?

range Medium
A. Remove the minimum score
B. Add only to the minimum
C. Add to every score
D. Double only the maximum

31 For the ordered data set , using the median-of-halves method, what is the interquartile range?

interquartile and the semi-interquartile range Medium
A.
B.
C.
D.

32 If and , what are the interquartile range and semi-interquartile range?

interquartile and the semi-interquartile range Medium
A. and
B. and
C. and
D. and

33 Which statement best explains why the interquartile range is often useful for skewed psychological data?

interquartile and the semi-interquartile range Medium
A. It ignores the middle half
B. It uses every score equally
C. It is less affected by extreme scores
D. It always equals the standard deviation

34 For the scores and , what is the average deviation from the mean?

the average deviation Medium
A.
B.
C.
D.

35 A distribution has mean , and the absolute deviations from the mean are and . What is the average deviation?

the average deviation Medium
A.
B.
C.
D.

36 Why are absolute values used when calculating the average deviation from the mean?

the average deviation Medium
A. To increase the number of observations
B. To preserve the original mean
C. To prevent positive and negative deviations from canceling
D. To make all scores identical

37 For the population scores and , what are the variance and standard deviation?

the standard deviation and variance Medium
A. Variance , standard deviation
B. Variance , standard deviation
C. Variance , standard deviation
D. Variance , standard deviation

38 A data set has a variance of . What is its standard deviation?

the standard deviation and variance Medium
A.
B.
C.
D.

39 If every score in a data set is multiplied by , how does the standard deviation change?

the standard deviation and variance Medium
A. It is multiplied by
B. It is multiplied by
C. It is divided by
D. It remains unchanged

40 Two samples have the same mean. Sample A has standard deviation , while Sample B has standard deviation . Which conclusion is justified?

the standard deviation and variance Medium
A. Sample B has greater variability
B. Both samples have equal ranges
C. Sample B has the larger mean
D. Sample A has greater variability

41 Group A contains 12 participants with a mean score of , while Group B contains 8 participants with a mean score of . What is the mean score for all 20 participants?

the mean Hard
A.
B.
C.
D.

42 A dataset has a mean of . Every score is transformed using . What are the mean and standard deviation of the transformed scores if the original standard deviation is ?

the mean Hard
A. Mean , SD
B. Mean , SD
C. Mean , SD
D. Mean , SD

43 The mean of five scores is . Four of the scores are , , , and . What score must be added as the fifth value?

the mean Hard
A.
B.
C.
D.

44 For the ordered dataset , an additional score is inserted. Which condition guarantees that the new median is ?

the median Hard
A.
B.
C.
D.

45 Which statement best explains why the median is preferred to the mean when summarizing a positively skewed income distribution?

the median Hard
A. It is less influenced by extreme high scores
B. It uses every score equally
C. It is unaffected by sample size
D. It always has a smaller numerical value

46 A sample contains the ordered scores . If the largest score is mistakenly recorded as , which measure changes most substantially?

the median Hard
A. The number of observations
B. The lower quartile
C. The mean
D. The median

47 The scores are . Which description of the mode is most accurate?

the mode Hard
A. The data are trimodal
B. The mode is
C. The mode is
D. The mode is

48 A researcher records response times as . If one additional response time of is recorded, what happens to the mode?

the mode Hard
A. It changes from to
B. It remains
C. It becomes undefined
D. It becomes bimodal at and

49 Which feature makes the mode especially useful for a nominal psychological variable such as preferred therapy type?

the mode Hard
A. It identifies the most frequent category
B. It requires numerical distances
C. It uses the central ranked observation
D. It minimizes squared deviations

50 A dataset has a minimum of and a maximum of . Every observation is transformed using . What is the new range?

range Hard
A.
B.
C.
D.

51 Two datasets have the same minimum and maximum but very different internal distributions. Which conclusion is justified?

range Hard
A. They have identical variances
B. They have identical interquartile ranges
C. They have identical ranges
D. They have identical medians

52 Using the median-of-halves convention, find the interquartile range and semi-interquartile range for .

interquartile and the semi-interquartile range Hard
A. IQR , SIQR
B. IQR , SIQR
C. IQR , SIQR
D. IQR , SIQR

53 A distribution has and . If every score is transformed by , what is the transformed interquartile range?

interquartile and the semi-interquartile range Hard
A.
B.
C.
D.

54 A study reports a median of and a semi-interquartile range of . Which interval represents the middle 50% of scores?

interquartile and the semi-interquartile range Hard
A.
B.
C.
D.

55 For the scores , what is the mean absolute deviation about the mean?

the average deviation Hard
A.
B.
C.
D.

56 For the scores , which statement correctly compares average deviation about the mean and about the median?

the average deviation Hard
A. Median-based deviation is smaller
B. Mean-based deviation is smaller
C. They are equal at
D. They are equal at

57 Treating the values as a population, which pair gives the variance and standard deviation?

the standard deviation and variance Hard
A. Variance , SD
B. Variance , SD
C. Variance , SD
D. Variance , SD

58 A sample has variance . If all scores are multiplied by and then increased by , what is the new variance?

the standard deviation and variance Hard
A.
B.
C.
D.

59 Two equal-sized groups each contain five scores. Group A has mean and population variance ; Group B has mean and population variance . What is the population variance of the combined ten scores?

the standard deviation and variance Hard
A.
B.
C.
D.

60 Which change to a dataset leaves the standard deviation unchanged while changing the mean?

the standard deviation and variance Hard
A. Multiply every score by
B. Add the same constant to every score
C. Replace each score with its square
D. Add a different constant to each score
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