TopicFurther Maths
Statistics & probability · SS1–SS3
Statistics & correlation
Statistics at Further Maths depth: measures of spread, scatter diagrams and correlation.
- Before this
- Dispersion & cumulative frequency
Learn
- 1Mean and standard deviation by the assumed meanThe assumed mean method for the mean, variance and standard deviation of lists and grouped tables, and finding missing values from a given mean or standard deviation.Done18 min
- 2Histograms, the mode and ogivesHistograms with unequal class widths (frequency density), the mode read from a histogram, and ogives for the median, quartiles, percentiles and 'how many between'.Done18 min
- 3Correlation and lines of best fitSpearman's rank correlation coefficient from ranks or raw scores, what the value means, scatter diagrams, and a line of best fit through the mean point.Done16 min
Flashcards
10 cards: the rules, facts and methods to know by heart, with the diagrams from the lessons. They come back until you know them.
Practise
Answer statistics & correlation 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 (65)
From 2008–2023: 62 WAEC, 3 NECO. Theory questions first, then objective, newest first.
Theory (56)
- NECO 2023 · Paper 2 · Q6The table shows the distribution of marks obtained by 100 candidates in an examination. Calculate, correct to three significant figures, the …
- WAEC 2023 · Paper 2 · Q13The mean of four consecutive odd numbers is 6. Find, correct to one decimal place, their variance.
- WAEC 2023 · Paper 2 · Q5The table shows the frequency distribution of a set of data.
- WAEC 2022 · Paper 2 · Q13| | 14 | 16 | 17 | 18 | 22 | 24 | 27 | 28 | 31 | 33 |
- WAEC 2022 · Paper 2 · Q6| Vocal () | 63 | 69 | 72 | 59 | 82 | 91 | 95 | 68 |
- WAEC 2022 · Paper 2 · Q12The mean and the standard deviation of marks scored by eight people in an interview are 7 and respectively. If six of the marks …
- WAEC 2022 · Paper 2 · Q5| Weight (N) | 40–46 | 47–53 | 54–60 | 61–67 | 68–74 | 75–81 | 82–88 | 89–95 |
- WAEC 2020 · Paper 2 · Q13| Class interval | 1–10 | 11–20 | 21–30 | 31–40 | 41–50 | 51–60 | 61–70 |
- WAEC 2020 · Paper 2 · Q6Using an assumed mean of , calculate the mean of and .
- WAEC 2019 · Paper 2 · Q13In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the …
- WAEC 2019 · Paper 2 · Q7| Age (years) | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 |
- WAEC 2019 · Paper 2 · Q12| Marks | 50–54 | 55–59 | 60–64 | 65–69 | 70–74 | 75–79 | 80–84 | 85–89 |
- WAEC 2019 · Paper 2 · Q6| Mass (kg) | 10.5–14.4 | 14.5–24.4 | 24.5–44.4 | 44.5–47.4 | 47.5–49.4 |
- WAEC 2019 · Paper 2 · Q12| Marks | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2019 · Paper 2 · Q6| Wages ($) | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 | 100–109 | 110–119 |
- WAEC 2018 · Paper 2 · Q12| Number of heads | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
- WAEC 2018 · Paper 2 · Q5| Cooking oil | A | B | C | D | E | F | G | H |
- WAEC 2018 · Paper 2 · Q12The data show the production of mobile phones per day over a thirty-day period by a company. 53 26 21 28 38 46 35 31 51 35 23 38 46 24 44 36 …
- WAEC 2018 · Paper 2 · Q6| Geography | 6 | 5 | 4 | 3 | 2 | 7 | 1 |
- WAEC 2018 · Paper 2 · Q12| Candidate | A | B | C | D | E | F | G | H | I | J |
- WAEC 2018 · Paper 2 · Q6| Age (years) | 20–24 | 25–29 | 30–34 | 35–39 | 40–44 | 45–49 | 50–54 | 55–59 |
- WAEC 2017 · Paper 2 · Q13| Age (years) | 17–19 | 20–22 | 23–28 | 29–34 | 35–43 |
- WAEC 2017 · Paper 2 · Q6| Height (cm) | 36–40 | 41–45 | 46–50 | 51–55 | 56–60 |
- WAEC 2017 · Paper 2 · Q12| Marks | 0–2 | 3–5 | 6–8 | 9–11 | 12–14 | 15–17 |
- WAEC 2017 · Paper 2 · Q6| Age (years) | 15–18 | 19–22 | 23–26 | 27–30 | 31–34 | 35–38 |
- WAEC 2016 · Paper 2 · Q12| Marks | 1–10 | 11–20 | 21–30 | 31–40 | 41–50 | 51–60 | 61–70 | 71–80 | 81–90 | 91–100 |
- WAEC 2016 · Paper 2 · Q6The mean of the numbers and is . Calculate the:
- WAEC 2016 · Paper 2 · Q13Using an assumed mean of 40, find the standard deviation of the following set of numbers: 28, 31, 32, 37, 40, 42, 45, 46, 48 and 50.
- WAEC 2016 · Paper 2 · Q6The scores of 20 students are: 3, 2, 4, 2, 3, 2, 1, 2, 2, 4, 5, 2, 5, 3, 1, 2, 2, 6, 2, 3.
- WAEC 2014 · Paper 2 · Q12The histogram represents the scores of some candidates in an examination.
- WAEC 2014 · Paper 2 · Q7The table shows the distribution of the lengths of 20 iron rods measured in metres.
- WAEC 2014 · Paper 2 · Q12| Age (years) | 15–19 | 20–24 | 25–29 | 30–34 | 35–39 | 40–44 | 45–49 | 50–54 | 55–59 | 60–64 |
- WAEC 2014 · Paper 2 · Q6The deviations from the mean of a set of numbers are , , , and , where is a constant. Find the value …
- WAEC 2013 · Paper 2 · Q13| Number of days () | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
- WAEC 2013 · Paper 2 · Q14A bag contains 5 blue, 4 green and 3 yellow balls. All the balls are identical except for colour. Three balls are drawn at random without replacement. …
- WAEC 2013 · Paper 2 · Q6| Age (years) | 12–14 | 15–17 | 18–20 | 21–23 | 24–26 |
- WAEC 2013 · Paper 2 · Q13A committee of 6 is to be selected at random from a group of 7 boys and 4 girls. (i) In how many ways can this be done if there are no restrictions? …
- WAEC 2013 · Paper 2 · Q14The mean of the numbers , , , , and is and their standard deviation is . Find the values of and .
- WAEC 2013 · Paper 2 · Q7The deviations of 85 from some numbers are , , , , , , , and . Find, correct to two decimal places, the:
- WAEC 2012 · Paper 2 · Q14The marks scored by forty candidates in an examination are shown in the table.
- WAEC 2011 · Paper 2 · Q14The table shows the frequency distribution of marks scored by some candidates in an examination.
- WAEC 2011 · Paper 2 · Q7A tyre manufacturing company researched into the life span of one type of their motorcycle tyres. The results were as follows:
- WAEC 2011 · Paper 2 · Q14The number of cars that called at a petrol station on some days of a month is as shown in the table.
- WAEC 2011 · Paper 2 · Q6In a physics examination, the mean mark of the first twelve students in a class is 60, that of the next twenty students is 50 and that of the …
- WAEC 2010 · Paper 2 · Q13The table shows the marks obtained by 40 students in a test.
- WAEC 2010 · Paper 2 · Q6The table gives the distribution of heights, in metres, of 100 students of the same age group.
- WAEC 2009 · Paper 2 · Q14The distribution of the lives (in days) of 40 transistor batteries is shown in the table.
- WAEC 2009 · Paper 2 · Q15The table shows the corresponding values of two variables and .
- WAEC 2009 · Paper 2 · Q14The age distribution of final year students in a polytechnic is shown in the table below.
- WAEC 2009 · Paper 2 · Q15In a test, eight students obtained the following marks in Biology and Physics.
- WAEC 2009 · Paper 2 · Q5The table shows the marks obtained by a group of students.
- WAEC 2008 · Paper 2 · Q14The following table shows the distribution of marks (%) obtained by some students in an examination.
- WAEC 2008 · Paper 2 · Q15Five (5) female and seven (7) male teachers applied for 4 vacancies in a Junior High School. The teachers are equally qualified. Find the number …
- WAEC 2008 · Paper 2 · Q6The table shows the distribution of marks obtained by some candidates in a test.
- WAEC 2008 · Paper 2 · Q13The table shows the examination marks of 8 students in Algebra and Statistics tests.
- WAEC 2008 · Paper 2 · Q5The deviations of a set of numbers from 55 are and . Calculate the:
Objective (9)
- NECO 2023 · Paper 1 · Q45The table shows the scores of students in a Mathematics examination. Find the lower class boundary of the class containing the sixth decile.
- NECO 2023 · Paper 1 · Q46Using the same table, what is the modal score?
- WAEC 2023 · Paper 1 · Q16The table shows the marks obtained by students in a test.
- WAEC 2023 · Paper 1 · Q29Adu's scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
- WAEC 2022 · Paper 1 · Q22The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
- WAEC 2022 · Paper 1 · Q23The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
- WAEC 2022 · Paper 1 · Q28The mean heights of three groups of students consisting of 20, 16 and 14 students each are 1.67 m, 1.50 m and 1.40 m respectively. Find …
- WAEC 2020 · Paper 1 · Q16Find the median of the numbers 9, 7, 5, 2, 12, 9, 9, 2, 10, 10 and 18.
- WAEC 2020 · Paper 1 · Q31Calculate the variance of , and .