Measures of variability

1. The standard error of measurement is used to estimate ...........

• Answer: b. student's true score
  The standard error of measurement (SEM) quantifies the amount of error associated with a test score, allowing educators to estimate a student's true score within a certain range.

2. The SEmeas is ...........

• Answer: c. greatly influenced by changes in correlation coefficient
  The standard error of measurement is affected by the reliability of the test; as the correlation coefficient increases (indicating higher reliability), the SEM decreases, reflecting more accurate measurements.

3. A large variance in a distribution means that ...........

• Answer: c. the sample is not homogenous
  A large variance indicates that scores are spread out over a wide range, suggesting diversity within the sample rather than uniformity.

4. Of the two tests, the one which yields a .......... is the one which is more reliable.

• Answer: d. lower standard deviation
  A lower standard deviation indicates that test scores are more closely clustered around the mean, suggesting greater reliability in measuring what they intend to assess.

5. The amount of dispersion of scores in a central value can be measured by the ...........

• Answer: d. standard deviation
  Standard deviation quantifies how much scores deviate from the mean, providing a clear measure of dispersion.

6. In a distribution like (1,8,10,12,16,18), the examiner would prefer the ...........

• Answer: a. median over the mean
  In this case, extreme values could skew the mean; thus, the median provides a better measure of central tendency that is less affected by outliers.

7. The easiest way to determine the spread of scores is by obtaining the ...........

• Answer: b. range
  The range is calculated simply as the difference between the highest and lowest scores, making it an easy measure to compute.

8. The median of the distribution 3, 2, 0, 1, 6 is ......

• Answer: c. 2
  To find the median: arrange in order: 0, 1, 2, 3, 6; since there are five numbers, the median is the middle value (2).

9. When scores and their frequencies are illustrated with points connected by lines it is called a frequency ..........

• Answer: c. polygon
  A frequency polygon connects points representing frequencies at specific intervals with lines to visualize data trends over intervals.

10. If the center of gravity of the distribution is shifted to one side of the curve, the curve becomes ..........

• Answer: a. skewed
  When one tail of a distribution is longer or fatter than another, it indicates that data are not symmetrically distributed and thus skewed.

11. We usually prefer the median to other measures of central tendency when there exist ······ ·.

• Answer: b. extreme scores at either end of the distribution
  The median is less affected by extreme values than the mean and thus provides a better central tendency measure in skewed distributions.

12. In a test, there were 100 questions, each consisting of three choices. One of the students answered 80 questions out of which as many as 20 were incorrect. After applying the chance guessing formula, the student's score would be ..........

• Answer: b. 30
  To calculate: Correct answers = Total answered - Incorrect = 80−20=6080−20=60; expected score from guessing = 803≈26.67380​≈26.67; thus total score = 60−≈26.67≈3360−≈26.67≈33.

13. One of the measures of central tendency which divides ranked scores into two halves is called the .......

• Answer: a. median
  The median divides a dataset into two equal halves when arranged in order.

14. If a constant is added to every score in a distribution, which of the following measures will not change?

• Answer: d. The range, mode and median
  Adding a constant affects measures like mean but does not change range or mode since they are based on relative positions.

15. In a distribution with extreme scores, which of the following statistics is more representative of the sample?

• Answer: d. median
  The median provides a better representation in skewed distributions as it minimizes distortion from extreme values.

16. As a measure of central tendency, the median is preferred to the mean when the distribution ……….

• Answer: b. yields a mean higher than median
  This often indicates positive skewness where extreme high values affect mean more than median.

17. The spread of scores can be best determined by ……….

• Answer: c. obtaining the SD
  Standard deviation gives detailed insight into score dispersion around the mean compared to simpler measures like range.

18. When all scores in a group occur with same frequency, it is customary to say that ..........

• Answer: d. the distribution has no mode
  If all values occur equally often, there’s no single value that appears more frequently than others; hence no mode exists.

19. A test was administered to a small class; following scores were obtained: 12,14,15,13,11; standard deviation is ..........

• Answer: b. 1.24
  To calculate SD: find mean (12), deviations from mean (e.g., -1,-0,-1,+1,+2), square deviations (e.g., +1,+0,+1,+0,+4), sum squared deviations (6), divide by N (5), take square root for SD (1.2≈1.241.2​≈1.24).

20. Using data: 12,14,15,13,11; What is SEM when r = .64?

• Answer: c .84
  Standard Error Mean (SEM) can be calculated using formula: SEM=SDnSEM=n​SD​. Assuming SD calculated previously as approximately 11 and n=5 gives SEM=15≈.84SEM=5​1​≈.84.

21. The standard error of measurement is used ............. .

• Answer: c. for probabilistic interpretations
  The standard error of measurement (SEM) provides an estimate of the range within which a student's true score is likely to fall, allowing for probabilistic interpretations of test scores.

22. The SD can be smaller than V when ……….

• Answer: d. V < 1
  Variance (V) is the square of the standard deviation (SD). Therefore, if the variance is less than 1, it implies that the standard deviation must also be less than 1.

23. The changes in subjects’ observed scores ……….

• Answer: c. are due to standard error of measurement
  Observed scores can fluctuate due to various factors, including measurement error, which is quantified by the standard error of measurement.

24. Which of the following is most likely not true?

• Answer: b. X > T
  In measurement theory, X represents the observed score and T represents the true score. It is not universally true that an observed score will always exceed the true score; it can be equal or less as well.

25. We can have a smaller SEM ……….

• Answer: d. when the test is highly reliable
  A higher reliability coefficient results in a smaller SEM, indicating that test scores are more stable and accurate reflections of a student's true ability.

26. The .......... estimates the limits within which an individual's obtained score on a test is likely to diverge from his/her true score.

• Answer: b. SEM
  The standard error of measurement provides a range around an observed score that indicates where the true score is likely to fall, based on the reliability of the test.

27. The ratio of the true score variance to observed score variance is called ..........

• Answer: d. reliability
  Reliability measures how consistently a test measures what it intends to measure, expressed as the ratio of true score variance to total observed score variance.

28. The standard error of measurement is used to estimate the .......... .

• Answer: d. student's true score
  The SEM indicates how much a student's observed score might differ from their true score due to measurement error.

29. The standard error of measurement is ...........

• Answer: c. greatly influenced by the correlation coefficient
  The SEM is affected by the reliability (correlation coefficient) of a test; higher reliability results in lower SEM values.

30. If the SD for class A is 4.08 and for class B is 8.9, one can conclude that ...........

• Answer: c. class A is more homogenous than class B
  A smaller standard deviation indicates that scores in class A are closer to each other (more homogenous) compared to class B, where scores are more spread out.

31. The limits within which an individual's obtained score on a test is likely to diverge from his true score is estimated by the ...........

• Answer: c. standard error of measurement
  The SEM provides a range indicating how much an individual's observed test score may vary from their actual ability due to errors in measurement.

32. The type of statistic which estimates the limits within which an individual's obtained score on a test is likely to diverge from his true score is called ...........

• Answer: b. standard error of measurement
  This statistic quantifies uncertainty in observed scores and helps interpret individual performance relative to their potential true ability.

33. What is the range of the true score of an examinee who got 25 on a test if the standard error of measurement (SEM) is 2?

• Answer: a. 21-29
  The range around the obtained score (25) would be calculated as: 25−225−2 to 25+225+2, resulting in a range from 23 to 27.

34. The standard error of measurement (SEM) of a test of vocabulary is ………. when the reliability is 0.75 and the variance is 4.

• Answer: c. 1
  To calculate SEM: SEM=SD×1−rSEM=SD×1−r​; here, SD=4=2SD=4​=2 and r=0.75r=0.75. Thus, SEM=2×1−0.75=2×0.25=2×0.5=1SEM=2×1−0.75​=2×0.25​=2×0.5=1.

35. The measures of dispersion are ...........

• Answer: c. range, standard deviation and variance
  These three statistics describe how spread out scores are within a dataset, indicating variability among scores.

36. The difference between the highest and lowest score in a distribution is termed as ...........

• Answer: a. range
  The range measures dispersion by calculating the difference between maximum and minimum values in a dataset.

37. The .......... is usually calculated by subtracting the lowest score from the highest score.

• Answer: a. range
  This calculation directly defines how spread out values are across a dataset by identifying extremes.

38. The average squared deviation around the mean of a distribution is called ...........

• Answer: b. variance
  Variance quantifies how much scores deviate from their mean value on average, providing insight into data spread.

39. An estimate of the average deviation around the mean of a normal distribution is called ...........

• Answer: b. standard deviation
  Standard deviation represents how much individual data points typically differ from the mean in terms of distance.

40. Another name for the square root of the variance is ...........

• Answer: a. standard deviation
  Standard deviation derives directly from variance as its square root, providing insights into data dispersion around the mean.

41. .......... is the standard deviation of the errors of measurement in a psychological test.

• Answer: c. Standard error of measurement
  The standard error of measurement (SEM) quantifies the amount of error associated with a test score. It indicates how much a person's observed score is expected to vary from their true score due to measurement error. SEM is particularly important in psychological testing, as it helps interpret individual scores in the context of reliability.

42. "Range" and "standard deviation" that show the spread of scores are called ...........

• Answer: b. measures of dispersion
  Both range and standard deviation are measures of dispersion, which describe how spread out the scores are in a dataset. The range provides a simple measure by subtracting the lowest score from the highest, while standard deviation gives a more detailed view by indicating how much individual scores deviate from the mean.

43. The mean of the squared variations around the mean is called ...........

• Answer: b. variance
  Variance is defined as the average of the squared deviations from the mean. It provides a measure of how much scores in a dataset differ from the mean, and it is essential for understanding data variability.

44. The standard error of measurement is used to estimate ...........

• Answer: b. student's true score
  The standard error of measurement helps estimate an individual's true score by providing a range within which their observed score may fall, accounting for potential measurement errors. This is crucial for interpreting test results accurately.