TopicGeneral Maths
Statistics & probability · SS2–SS3
Dispersion & cumulative frequency
How spread out data is: range, deviation, quartiles and the cumulative frequency curve.
- Before this
- Statistics: data & averages
- Leads to
- Statistics & correlation
Learn
- 1Range, quartiles and standard deviationHow spread out data is: the range and interquartile range, the mean deviation, and the variance and standard deviation, from a list and from a frequency table.Done26 min
- 2The cumulative frequency curveBuilding the cumulative frequency table, plotting at upper class boundaries, drawing the ogive, and reading medians, quartiles, percentiles and counts from it.Done22 min
Practise
Answer dispersion & cumulative frequency questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
Your progress is saved on this device as you practise. No account needed.
Past questions (86)
From 1984–2025: 41 WAEC, 7 NECO, 38 JAMB. Theory questions first, then objective, newest first.
Theory (35)
- WAEC 2025 · Paper 2 · Q11The table shows the scores of 2000 candidates in an examination.
- NECO 2024 · Paper 2 · Q4Given the numbers 2, 6, 9, 8, 7, 9, 8, 7, calculate, correct to 2 decimal places, the:
- NECO 2023 · Paper 2 · Q12The scores of students in a Biology test in a particular school are 12, , 15, , 25, 12, 30, 15, 25, 12, 16 and 12. If the mean score is …
- WAEC 2023 · Paper 2 · Q9| Height (m) | 3 | 4 | 5 | 6 | 7 | 8 |
- WAEC 2023 · Paper 2 · Q11The table shows the frequency distribution of the ages of fifty members of a family.
- WAEC 2023 · Paper 2 · Q5The heights (in cm) of 10 students in a class are: and . Find the:
- WAEC 2022 · Paper 2 · Q10| Age (years) | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
- WAEC 2022 · Paper 2 · Q11| Age (years) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
- WAEC 2022 · Paper 2 · Q11| Marks | 2 | 3 | 4 | 5 | 6 |
- WAEC 2021 · Paper 2 · Q11| Number of hours per day | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
- WAEC 2021 · Paper 2 · Q10| Mark (%) | 1–10 | 11–20 | 21–30 | 31–40 | 41–50 | 51–60 | 61–70 | 71–80 | 81–90 | 91–100 |
- WAEC 2021 · Paper 2 · Q5| Age | 12 | 13 | 15 | 10 | 14 | 16 |
- WAEC 2020 · Paper 2 · Q10| Marks (%) | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2020 · Paper 2 · Q3The ages of some lecturers are 42, 54, 50, 54, 50, 42, 46, 46, 48 and 48. Calculate the:
- WAEC 2020 · Paper 2 · Q10The ages of 14 children at a party are given as follows: 12, 6, 5, 4, 8, 13, 11, 2, 5, 7, 1, 9, 10 and 3.
- WAEC 2019 · Paper 2 · Q7The data show the marks obtained by students in a Biology test. 50 56 25 56 68 73 66 64 56 48 20 39 9 50 46 54 54 40 50 96 36 44 18 97 65 21 …
- WAEC 2019 · Paper 2 · Q7The following are the scores of 48 students in a promotion test. 52 56 25 56 68 73 66 64 56 48 15 88 20 39 9 50 98 54 54 40 50 96 53 16 36 44 …
- WAEC 2018 · Paper 2 · Q13| Marks | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |
- WAEC 2018 · Paper 2 · Q5If the mean of , , , and is 12, calculate the mean of , , , and .
- WAEC 2018 · Paper 2 · Q3| Price (₦1,000,000) | 1.0–1.9 | 2.0–2.9 | 3.0–3.9 | 4.0–4.9 | 5.0–5.9 |
- WAEC 2018 · Paper 2 · Q9| Marks (%) | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2017 · Paper 2 · Q8| Marks | 1 | 2 | 3 | 4 | 5 |
- WAEC 2016 · Paper 2 · Q9The weight (in kg) of 50 contestants at a competition is as follows: 65 66 67 66 64 66 65 63 65 68 64 62 66 64 67 65 64 66 65 67 65 67 66 64 …
- WAEC 2016 · Paper 2 · Q12| Marks | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
- WAEC 2015 · Paper 2 · Q13| Marks (%) | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2014 · Paper 2 · Q11| Score | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2014 · Paper 2 · Q11The probabilities that Manful, John and Ernest will pass an examination are , and respectively. Find the probability …
- WAEC 2013 · Paper 2 · Q11| Marks (%) | 1–10 | 11–20 | 21–30 | 31–40 | 41–50 | 51–60 | 61–70 | 71–80 | 81–90 | 91–100 |
- WAEC 2013 · Paper 2 · Q9Solve: .
- WAEC 2012 · Paper 2 · Q10| Marks | 60–64 | 65–69 | 70–74 | 75–79 | 80–84 | 85–89 | 90–94 | 95–99 |
- WAEC 2012 · Paper 2 · Q12The ages (in years) of men selected from a community are as follows: 44 28 58 50 93 35 34 52 57 61 40 63 90 67 64 56 51 82 73 43 73 73 44 71 …
- WAEC 2011 · Paper 2 · Q11| Score | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2010 · Paper 2 · Q12The frequency distribution of the weight of 100 participants in a high jump competition is as shown below.
- WAEC 2010 · Paper 2 · Q10The table gives the distribution of marks for 360 candidates who sat for an examination.
- WAEC 2009 · Paper 2 · Q3The table shows the number of children per family in a community.
Objective (51)
- NECO 2024 · Paper 1 · Q52Find the range of 4, 9, 6, 3, 2, 8, 10, 7, 11.
- NECO 2024 · Paper 1 · Q53Calculate the variance of 30, 28, 35, 25, 37.
- WAEC 2024 · Paper 1 · Q40The masses (in kg) of members in a club are 59, 44, 53, 57, 49, 40, 48 and 50. Calculate the variance of the distribution.
- WAEC 2024 · Paper 1 · Q48Find the range of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15 and 25.
- NECO 2023 · Paper 1 · Q49Calculate the mean deviation of the scores 4, 5, 3, 2, 1.
- WAEC 2023 · Paper 1 · Q25Find the mean deviation of the numbers 14, 15, 16, 17, 18, 19.
- NECO 2022 · Paper 1 · Q53The mean of the following set of data: 5, 7, 9, and 6 is 6. Find the variance.
- NECO 2022 · Paper 1 · Q57Find the range of the following set of numbers: 8, 10, 2, 6, 16, 24, 12, 20.
- WAEC 2022 · Paper 1 · Q38The ages in years of some members of a singing group are 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the lower quartile.
- WAEC 2021 · Paper 1 · Q35Find the first quartile of 7, 8, 7, 9, 11, 8, 7, 9, 6 and 8.
- WAEC 2020 · Paper 1 · Q35The mean of the numbers 15, 21, 17, 26, 18 and 29 is 21. Calculate the standard deviation.
- WAEC 2020 · Paper 1 · Q47The interquartile range of a distribution is 7. If the 25th percentile is 16, find the upper quartile.
- WAEC 2019 · Paper 1 · Q41Calculate the variance of 2, 4, 7, 8 and 9.
- JAMB 2017 · UTME · Q4Calculate the mean deviation of the numbers 7, 3, 14, 9, 7 and 8.
- JAMB 2017 · UTME (set 2) · Q14Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5.
- JAMB 2017 · UTME (set 2) · Q35Find the range of the following set of numbers: 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2.
- JAMB 2016 · UTME · Q24Find the standard deviation of 2, 3, 5 and 6.
- JAMB 2014 · UTME · Q47Find the standard deviation of 5, 4, 3, 2, 1.
- JAMB 2013 · UTME · Q45If the variance of , , , and is 4 and the mean is 5, find the standard deviation.
- JAMB 2013 · UTME · Q46| Score | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
- JAMB 2012 · UTME · Q45Find the range of 4, 9, 6, 3, 2, 8, 10 and 11.
- JAMB 2012 · UTME · Q46Find the standard deviation of 2, 3, 8, 10 and 12.
- JAMB 2010 · UTME · Q48Find the standard deviation of 2, 3, 5 and 6.
- JAMB 2004 · UME · Q42The graph shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than …
- JAMB 2004 · UME · Q44The weights of 10 pupils in a class are 15 kg, 16 kg, 17 kg, 18 kg, 16 kg, 17 kg, 17 kg, 17 kg, 18 kg and 16 kg. What is the range of this distribution?
- JAMB 2004 · UME · Q45Find the mean deviation of 1, 2, 3 and 4.
- JAMB 2003 · UME · Q42The mean of the numbers 3, 6, 4, and 7 is 5. Find the standard deviation.
- JAMB 2003 · UME · Q45The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21 and 16 is
- JAMB 2002 · UME · Q23The range of the data and is
- JAMB 2002 · UME · Q30Calculate the mean deviation of the numbers 7, 3, 14, 9, 7 and 8.
- JAMB 2001 · UME · Q44Find the range of and .
- JAMB 2001 · UME · Q45Find the variance of 2, 6, 8, 6, 2 and 6.
- JAMB 2001 · UME · Q46A cumulative frequency graph shows the distribution of masses of fertilizer for 48 workers. Which of the following gives the interquartile range?
- JAMB 2000 · UME · Q42If the mean of the numbers , , and is 4, find their mean deviation.
- JAMB 2000 · UME · Q46The cumulative frequency curve represents the ages of 100 students in a school. Which age group do of the students belong to?
- JAMB 2000 · UME · Q47The variance of , , , and is
- JAMB 2000 · UME · Q48Find the sum of the range and the mode of the numbers 10, 5, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5.
- JAMB 1999 · UME · Q44If the standard deviation of the numbers 3, 6, , 7, 5 is , find the least possible value of .
- JAMB 1998 · UME · Q44Find the variance of the numbers , , .
- JAMB 1998 · UME · Q45Find the positive value of if the standard deviation of the numbers , , is .
- JAMB 1997 · UME · Q47Find the standard deviation of the data .
- JAMB 1997 · UME · Q48Find the difference between the range and the variance of the numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7, where .
- JAMB 1995 · UME · Q45Find the standard deviation of the data in the table below.
- JAMB 1995 · UME · Q46The variance of the scores 1, 2, 3, 4, 5 is
- JAMB 1994 · UME · Q46Find the mean deviation of the numbers 4, 5, 9.
- JAMB 1994 · UME · Q47Estimate the median of the frequency distribution below.
- JAMB 1993 · UME · Q47Find the median of the observations in the table below.
- JAMB 1993 · UME · Q49Calculate the standard deviation of the data 7, 8, 9, 10, 11, 12, 13.
- JAMB 1992 · UME · Q45If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores.
- JAMB 1987 · UME · Q49The scores of a group of students in a music test are shown. If is the number of students with scores less than or equal to , find …
- JAMB 1984 · UME · Q37The cumulative frequency function of the data below is . What is ?