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Histogram,frequency distribution revision card
The document contains a series of histograms showing frequency distributions of test scores. It provides solutions to questions about analyzing the distributions, including identifying the modal class, range of scores, class boundaries, frequency within classes, total number of students, and number of students within certain score ranges. Key information that can be extracted from the histograms includes the class boundaries, frequencies, and identifying the class with the highest frequency to determine the mode.
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Histogram,frequency distribution revision card
- 1. HISTOGRAM A histogram usesbars of equal width with no spaces between them to represent information
- 2. SolutionJAMB 2003 𝐹𝑟𝑜𝑚 𝑡ℎ𝑒𝑞𝑢𝑒𝑠𝑡𝑖𝑜𝑛 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 120 ⇒ 12 + 20 + 𝑥 + 21 + 𝑥 − 1 + 28 = 120 ⇒ 80 + 2𝑥 = 120 ⇒ 2𝑥 = 40 ⇒ 𝑥 = 20
- 3. JAMB 2003 Solution 𝑁𝑢𝑚𝑏𝑒𝑟𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑤ℎ𝑜 𝑤𝑒𝑟𝑒 𝑖𝑛𝑣𝑜𝑙𝑣𝑒𝑑 𝑖𝑛 𝑡ℎe pollution = 3 + 4 + 5 + 6 + 2 = 20
- 4. JAMB 2014 Solution Themode is 4 since it is the number with the highest frequency.
- 5. JAMB 1997 Solution 𝑁𝑢𝑚𝑏𝑒𝑟𝑜𝑓 𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 𝑡ℎ𝑒 𝑠𝑐ℎ𝑜𝑜𝑜𝑙 𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑒𝑑 = 3 + 5 + 8 + 1 + 2 = 19
- 6. 1. The frequencydistribution of students in a test is given as follows. What is the modal class? A. 1 − 5 B. 6 − 10 C. 11 − 15 D. 16-20 E. 21-25 F. The correct answer is 16 − 20 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2
- 7. 1. The frequencydistribution of students in a test is given as follows. What is the modal class? A. 1 − 5 B. 6 − 10 C. 11 − 15 D. 16-20 E. 21-25 F. The correct answer is 16 − 20 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 16 − 20
- 8. 2. The frequencydistribution of students in a test is given as follows. What is the range of the class score? A. 29 B. 25 C. 11 D. 21 E. 24 The correct answer is 29 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2
- 9. 2. The frequencydistribution of students in a test is given as follows. What is the range of the class score? A. 29 B. 25 C. 11 D. 21 E. 24 The correct answer is 29 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2 Solution Range= highest score – lowest score = 30 − 1 = 29
- 10. 3. The frequencydistribution of students in a test is given as follows. What is the upper class boundary of the modal class? A. 29.5 B. 25.5 C. 19.5 D. 20.5 E. 21.5 The correct answer is 20.5 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2
- 11. 3. The frequencydistribution of students in a test is given as follows. What is the upper class boundary of the modal class? A. 29.5 B. 25.5 C. 19.5 D. 20.5 E. 21.5 The correct answer is 20.5 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 4 6 − 10 6 11 − 15 4 16 − 20 7 21 − 25 3 26 − 30 2 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠 ℎ𝑎𝑠 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑖𝑒𝑠 = 15.5 − 20.5 The upper class boundary=20.5
- 12. 4. The frequencydistribution of students in a test is given as follows. What is the modal score? A. 1 B. 2 C. 3 D. 4 E. 5 The correct answer is 2 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 4 2 6 3 4 4 1 5 3 6 2
- 13. 4. The frequencydistribution of students in a test is given as follows. What is the modal score? A. 1 B. 2 C. 3 D. 4 E. 5 The correct answer is 2 𝑀𝑎𝑟𝑘𝑠 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 4 2 6 3 4 4 1 5 3 6 2 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑎𝑙 𝑠𝑐𝑜𝑟𝑒 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑐𝑜𝑟𝑒 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 2
- 14. 5. The frequencydistribution of students in a test is given as follows. What is the upper class boundary of the highest class? A. 29.5 B. 25.5 C. 19.5 D. 20.5 E. 30.5 The correct answer is 30.5 𝑀𝑎𝑟𝑘𝑠 Midpoint 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 3 4 6 − 10 8 6 11 − 15 13 4 16 − 20 18 7 21 − 25 23 3 26 − 30 28 2
- 15. 5. The frequencydistribution of students in a test is given as follows. What is the upper class boundary of the highest class? A. 29.5 B. 25.5 C. 19.5 D. 20.5 E. 30.5 The correct answer is 30.5 𝑀𝑎𝑟𝑘𝑠 Midpoint 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 1 − 5 3 4 6 − 10 8 6 11 − 15 13 4 16 − 20 18 7 21 − 25 23 3 26 − 30 28 2 Solution 𝑇ℎ𝑒 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑐𝑙𝑎𝑠𝑠 ℎ𝑎𝑠 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑖𝑒𝑠 = 25.5 − 30.5 The upper class boundary=30.5
- 16. 6. The histogrambelow represents the frequency distribution of students in a test. Estimate the mode? A. 29.5 B. 18.5 C. 19.5 D. 20.5 E. 17.5 The correct answer is 17.5
- 17. 6. The histogrambelow represents the frequency distribution of students in a test. Estimate the mode? A. 29.5 B. 18.5 C. 19.5 D. 20.5 E. 17.5 The correct answer is 17.5 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑛𝑑𝑠 𝑡𝑜 = 17.5
- 18. 7. The histogrambelow represents the frequency distribution of students in a test. What is the lower class boundary of the modal class? A. 29.5 B. 15.5 C. 19.5 D. 10.5 E. 17.5 The correct answer is 15.5
- 19. 7. The histogrambelow represents the frequency distribution of students in a test. What is the lower class boundary of the modal class? A. 29.5 B. 15.5 C. 19.5 D. 10.5 E. 17.5 The correct answer is 15.5 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠 ℎ𝑎𝑠 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑖𝑒𝑠 = 15.5 − 20.5 The lower class boundary=15.5
- 20. 8. The histogrambelow represents the frequency distribution of students in a test. How many students lie within the modal class? A. 2 B. 3 C. 4 D. 7 E. 8 The correct answer is 7
- 21. 8. The histogrambelow represents the frequency distribution of students in a test. How many students lie within the modal class? A. 2 B. 3 C. 4 D. 7 E. 8 The correct answer is 7 Solution 𝑇ℎ𝑒 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠 ℎ𝑎𝑠 𝑎 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 of 7
- 22. 9. The histogrambelow represents the frequency distribution of students in a test. How many students took the test? A. 26 B. 36 C. 46 D. 76 E. 86 The correct answer is 26
- 23. 9. The histogrambelow represents the frequency distribution of students in a test. How many students took the test? A. 26 B. 36 C. 46 D. 76 E. 86 The correct answer is 26 students Solution The number of students=4+6+4+7+3+2=26
- 24. 9. The histogrambelow represents the frequency distribution of students in a test. How many students scored at least 25.5? A. 2 B. 3 C. 4 D. 7 E. 8 The correct answer is 2
- 25. 9. The histogrambelow represents the frequency distribution of students in a test. How many students scored at least 25.5? A. 2 B. 3 C. 4 D. 7 E. 8 The correct answer is 2 Solution students who scored at least 25.5 are within 25.5 to 30.5=2
- 26. 10. The histogrambelow represents the frequency distribution of students in a test. How many students scored at most 10.5? A. 2 B. 3 C. 4 D. 10 E. 8 The correct answer is 10
- 27. 10. The histogrambelow represents the frequency distribution of students in a test. How many students scored at most 10.5? A. 2 B. 3 C. 4 D. 10 E. 8 The correct answer is102 Solution students who scored at most 10.5 are within 10.5 or less =4+6=10
- 28. SUMMARY You can alwaysconstruct a frequency distribution table from a histogram and Use it to answer related follow up questions.