Measures of central tendency

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

• Answer: b. has one or two extreme scores
  The median is less affected by extreme values (outliers) than the mean, making it a better measure of central tendency when such scores are present.

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

• Answer: c. has one or two extreme scores
  This reinforces that extreme values can skew the mean, while the median remains stable and accurately reflects the center of the data.

3. The two common measures of central tendency are the ...........

• Answer: d. mean and median
  The mean and median are widely recognized as primary measures of central tendency, providing insights into average performance and middle values in datasets.

4. The .......... is the most stable index of spread of scores or dispersion.

• Answer: c. standard deviation
  The standard deviation provides a consistent measure of variability around the mean, making it a reliable index for understanding score dispersion.

5. Variability of scores is reflected in the ...........

• Answer: d. range and standard deviation
  Both range (the difference between highest and lowest scores) and standard deviation (the average distance of each score from the mean) effectively illustrate how spread out scores are.

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, there are potential outliers that could skew the mean; thus, using the median gives a better representation of central tendency unaffected by extreme values.

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.

Answer

Here are the answers to your questions with detailed explanations for each correct choice:

21. What is the standard error of measurement of a vocabulary test with a reliability of 0.84 and a variance of 25?

• Answer: b. 2.5
  To calculate the standard error of measurement (SEM), use the formula:

SEM=SD×1−rSEM=SD×1−r​

Where SDSD (standard deviation) is the square root of variance. Here, SD=25=5SD=25​=5 and r=0.84r=0.84. Thus,

SEM=5×1−0.84=5×0.16=5×0.4=2SEM=5×1−0.84​=5×0.16​=5×0.4=2

22. When the reliability is 1, the value of standard error of measurement is ..........

• Answer: d. 0.0
  When reliability is perfect (1), it indicates that there is no error in measurement, leading to a standard error of measurement (SEM) of zero, meaning all scores are perfectly accurate.

23. The score gained by the middle candidate in the order of merit is referred to as ..........

• Answer: c. median
  The median is defined as the middle value in a ranked dataset, representing the score that divides the dataset into two equal halves.

24. The mode refers to the ...........

• Answer: b. score which most candidates obtained
  The mode is the value that appears most frequently in a dataset, indicating the most common score among candidates.

25. The mode, median, and the mean are called .......... .

• Answer: a. measures of central tendency
  These three statistics are used to summarize and describe the central point or typical value within a dataset.

26. The score obtained by the middle candidate in the order of merit is called ...........

• Answer: b. median
  As previously explained, the median represents the middle score when all scores are arranged in ascending or descending order.

27. In a normal distribution, the mean, median, and mode are ...........

• Answer: a. all the same
  In a perfectly normal distribution, these three measures of central tendency coincide at the center point of the distribution.

28. The .......... is obtained by summing scores across individual cases and dividing the sum by the number of cases. It is also called arithmetic average.

• Answer: a. mean
  The mean (or average) is calculated by adding all scores together and dividing by the total number of scores.

29. The point representing the 50th percentile in a distribution of scores, that is, the point that divides the distribution into upper and lower halves is called ...........

• Answer: b. median
  The median corresponds to the 50th percentile, indicating that half of all scores fall below this point.

30. .......... is the score in a distribution which occurs with greatest frequency.

• Answer: c. Mode
  The mode represents the most frequently occurring score within a dataset.