Grade 10 Maths · Statistics · Paper 2

Five Number Summary Grade 10

Real Five Number Summary past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 9 past paper questions
skills: 3 skills
videos: 3 videos

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Question 2.6 · November 2025 · Paper 2 · Provincial · 2 marks

The cumulative frequency graph presents data from a survey conducted in a certain restaurant, detailing the distribution of tips earned by employees during their shift. $Diagram for this question$

2.6 Calculate the interquartile range of the data.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

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More Five Number Summary Grade 10 questions and answers

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4. Question 1.4 · November 2024 · Paper 2 · Provincial · 3 marks
After utilising GeoGebra to teach geometry, the 14 participants marks out of 100 are displayed in the table below. $Diagram for this question$
1.4 Determine the interquartile range of the data.(3)
Show the memo (3 ticks)Memo
1. ✓
  $Q_{1}$ $Q_{1} = 41$
  1 mark · Find quartiles, range and IQR
2. ✓
  $Q_{3}$ $Q_{3} = 60$
  1 mark · Find quartiles, range and IQR
3. ✓
  Answer $I QR = Q_{3} - Q_{1} = 60 - 41$
  $= 19$
  1 mark · Find quartiles, range and IQR
5. Question 1.4.3 · November 2024 · Paper 2 · Provincial · 4 marks
The traffic department set up a roadblock on the N12 between Potchefstroom and Klerksdorp. During the first hour, they stopped 11 minibus taxis.
The following dataset is a summary of the number of passengers per minibus taxi.

18, 26, 25, 18, 16, 12, 10, 8, 18, 17, 8
1.4 During the second hour of the roadblock, a further 5 minibus taxis were stopped. The number of passengers in these 5 taxis are: $x$ , 13, 18, $y$ , 20.

These 5 numbers are already arranged from smallest to largest.

The entire dataset for the first and second hours is collectively represented on a box-and-whisker diagram. The new average number of passengers for the 16 taxis is 16. The five-number summary can be seen on the diagram below.

Answer the questions that follow. $Diagram for question 1.4$
1.4.3 Calculate the value of $x$ and $y$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Position of $Q_{3}$ $x$ , 8, 8, 10, 12, 13, 16, 17, 18, 18, 18, 18, $y$ , 20, 25, 26
  $Q_{3} = 19$
  $∴ \frac{3 ( 16 + 1 )}{4} = 12, 7 5^{t h}$ position
  1 mark · Find quartiles, range and IQR
2. ✓
  Value of $y$ Between 12th and 13th position
  $\frac{18 + y}{2} = 19$
  $∴ y = 20$
  1 mark · Find quartiles, range and IQR
3. ✓
  New mean equationNew $\overset{x}{ˉ}$ : $\frac{247 + x}{16} = 16$
  1 mark · Calculate the mean
4. ✓
  Value of $x$ $∴ x = 9$
  1 mark · Calculate the mean
6. Question WE10 · Siyavula Grade 10 Mathematics, 10.4 Measures of dispersion, Worked example 10 · 3 marks
WE10 Find the range of the following data set:
${1; 4; 5; 8; 6; 7; 5; 6; 7; 4; 10; 9; 10}$
What would happen if we removed the first value from the set?(3)
Show the memo (3 ticks)Memo
1. ✓
  RangeThe smallest value is $1$ and the largest value is $10$ .
  Range $= 10 - 1 = 9$
  1 mark · Find quartiles, range and IQR
2. ✓
  Range without the first valueIf $1$ were removed, the minimum would be $4$ .
  Range $= 10 - 4 = 6$
  1 mark · Find quartiles, range and IQR
3. ✓
  Effect of the outlier $1$ is not typical of the other values. It is an outlier and has a big influence on the range.
  1 mark · Interpret data and draw conclusions
7. Question WE14 · Siyavula Grade 10 Mathematics, 10.5 Five number summary, Worked example 14 · 6 marks
WE14 Draw a box and whisker diagram for the following data set:
${1, 25; 1, 5; 2, 5; 2, 5; 3, 1; 3, 2; 4, 1; 4, 25; 4, 75; 4, 8; 4, 95; 5, 1}$ (6)
Show the memo (6 ticks)Memo
1. ✓
  Minimum and maximumThe data set is already sorted: minimum $= 1, 25$ ; maximum $= 5, 1$ .
  1 mark · Find quartiles, range and IQR
2. ✓
  MedianThere are $12$ values, so the median lies between the sixth and seventh values:
  $\frac{3 , 2 + 4 , 1}{2} = 3, 65$
  1 mark · Find the median
3. ✓
  Lower quartileThe first quartile lies between the third and fourth values:
  $\frac{2 , 5 + 2 , 5}{2} = 2, 5$
  1 mark · Find quartiles, range and IQR
4. ✓
  Upper quartileThe third quartile lies between the ninth and tenth values:
  $\frac{4 , 75 + 4 , 8}{2} = 4, 775$
  1 mark · Find quartiles, range and IQR
5. ✓
  BoxFive number summary: $(1, 25; 2, 5; 3, 65; 4, 775; 5, 1)$ .
  On a number line, draw the box from $2, 5$ (lower quartile) to $4, 775$ (upper quartile) with a line across it at the median $3, 65$ .
  1 mark · Draw a box and whisker diagram
6. ✓
  WhiskersDraw the whiskers from the box out to the minimum $1, 25$ and the maximum $5, 1$ (see the diagram). $Memo diagram$
  1 mark · Draw a box and whisker diagram
8. Question a · Siyavula Grade 12 Mathematics, 9.1 Revision, Worked example 3 · 5 marks
Three Matric classes wrote a Mathematics test. The test is out of $40$ marks and each class has $21$ learners. The results of the test are shown in the table below: $Diagram for this question$
a For each class, determine the five number summary and draw a box and whisker diagram on the same set of axes using an appropriate scale.(5)
Show the memo (5 ticks)Memo
1. ✓
  Minimum and maximumThe data is already ordered. The minimum of each data set is $4$ and the maximum of each data set is $40$ .
  1 mark · Find quartiles, range and IQR
2. ✓
  MediansThere are $21$ values, so the median is the eleventh mark: $16$ for Gr. 12A, $32$ for Gr. 12B and $21$ for Gr. 12C.
  1 mark · Find the median
3. ✓
  Lower quartilesThe first quartile lies between the fifth and sixth values: $12$ for Gr. 12A, $16$ for Gr. 12B and $14$ for Gr. 12C.
  1 mark · Find quartiles, range and IQR
4. ✓
  Upper quartilesThe third quartile lies between the $1 6^{th}$ and $1 7^{th}$ values: $36$ for Gr. 12A and Gr. 12B, and $\frac{30 + 32}{2} = 31$ for Gr. 12C.
  1 mark · Find quartiles, range and IQR
5. ✓
  Box and whisker diagramsGr. 12A $= [4; 12; 16; 36; 40]$
  Gr. 12B $= [4; 16; 32; 36; 40]$
  Gr. 12C $= [4; 14; 21; 31; 40]$
  Draw the three box and whisker diagrams on the same scale from $0$ to $40$ (see the diagram). $Memo diagram$
  1 mark · Draw a box and whisker diagram

Five Number Summary Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Statistics Grade 10: QuartilesKevinmathscience

Statistics Grade 10: Box and whiskerKevinmathscience

6. Grade 11 Mathematics - Statistics - Skewed DataJuniorTukkie at the University of Pretoria

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