Ghana Teacher Licensure Examination · Numeracy

Educational Statistics, Percentiles and Assessment Metrics

35 practice questions, each with the answer and an explanation.

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All 35 questions

  1. A class of 10 students scored the following marks out of 20: 8, 12, 12, 14, 15, 15, 15, 17, 18, 19. What is the mode?
  2. Nine pupils recorded test scores of 45, 50, 52, 58, 60, 65, 70, 78, 85. What is the median score of the group?
  3. A student scored at the 75th percentile in a national standardized literacy assessment. How is this interpreted?
  4. In a symmetric bell-shaped normal distribution of 1,000 student scores with mean 50 and standard deviation 10, what percentage falls between 40 and 60?
  5. The mean mark of 20 boys was 65, while the mean mark of 30 girls was 75. What is the combined mean mark of all 50 pupils?
  6. If the variance of test scores in a class test is 36, what is the standard deviation?
  7. In an item analysis, an item difficulty index (p-value) of 0.85 indicates that the test item was:
  8. A test item has a discrimination index of -0.20. What action should the test developer take?
  9. The scores of five students on a quiz are 10, 14, 15, 17, and 19. What is the sample range of these scores?
  10. What is the lower quartile (Q1) of the set of scores: 12, 15, 18, 20, 22, 25, 28, 30?
  11. What is the interquartile range (IQR) for a test distribution where Q1 = 42 and Q3 = 78?
  12. A standardized test raw score is converted to a z-score using z = (X - μ) / σ. If X = 72, μ = 60, and σ = 8, what is z?
  13. T-score is defined as T = 50 + 10z. What is the T-score of a student whose z-score is -1.4?
  14. When a score distribution has a long tail extending toward the lower values (left), the distribution is described as:
  15. In a positively skewed distribution of class test results, which relationship among central tendencies holds true?
  16. A pupil scored 64 on a test with mean 56 and standard deviation 8. On a second test, mean was 70 and standard deviation 10. What equivalent score has the same z-score?
  17. A frequency table shows class intervals of width 5: 10-14, 15-19, 20-24. What is the class mark (midpoint) of 15-19?
  18. The mean of five numbers is 18. If a sixth number is added, the new mean becomes 20. What is the sixth number?
  19. In a school survey, 60% of 250 teachers hold a master's degree. How many teachers hold a master's degree?
  20. A cumulative frequency curve (ogive) is primarily utilized by educators to estimate which statistical measure?
  21. On a pie chart displaying pupil enrollment across 4 houses, Red House occupies a sector angle of 72°. What percentage of pupils belong to Red House?
  22. A box plot shows a box extending from 40 to 70 with a vertical line at 58, and whiskers at 25 and 90. What is the median?
  23. Which measure of central tendency is least affected by extreme outlier scores in a classroom examination?
  24. A teacher recorded these absences over 6 weeks: 2, 4, 4, 6, 8, 12. What is the mean absolute deviation (MAD) from the mean?
  25. If all student scores on a chemistry test are multiplied by a constant factor of 1.10, how does the standard deviation change?
  26. If a teacher adds 5 bonus marks to every student's score on a test, what happens to the standard deviation of the scores?
  27. What is the probability of randomly choosing a student scoring 80 or above from a class of 40 where 12 scored 80 or above?
  28. In a 40-item multiple choice test with 4 options per question, what is the expected guessing score for a purely random responder?
  29. A diagnostic assessment of 50 items has a Cronbach's alpha coefficient of 0.88. What does this coefficient measure?
  30. What is the standard error of measurement (SEM) if a test has a standard deviation of 6 and reliability coefficient r = 0.75?
  31. In an exam, student A scored 68 where class mean was 60 and SD was 4. Student B scored 75 where class mean was 65 and SD was 5. Compare their relative performances:
  32. A student receives scores of 70, 80, and 90 with weights of 20%, 30%, and 50% respectively. What is the weighted average?
  33. What percentage of scores in a normal distribution fall within two standard deviations of the mean (between μ - 2σ and μ + 2σ)?
  34. The upper quartile of a class test is 74 and the lower quartile is 54. What is the semi-interquartile range?
  35. A scatter plot of pupils' study hours versus exam scores shows points sloping tightly from lower left to upper right. What correlation does this demonstrate?

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