Grade 10 Maths · Statistics · Paper 2

Measures of Dispersion Grade 10

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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)

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More Measures of Dispersion Grade 10 questions and answers

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4. Question 5.2.3 · September 2024 · Provincial · 3 marks
The following Life Sciences marks, for a test out of 50, were recorded from 15 grade 10 learners at a certain school.
5.2 Determine:
5.2.3 The interquartile range.(3)
Show the memo (2 ticks)Memo
1. ✓
  $29 - 17$ (double tick) $Q_{1} = 17$ , $Q_{3} = 29$ : $IQR = 29 - 17$
  2 marks · Find quartiles, range and IQR
2. ✓
  Answer $= 12$
  1 mark · Find quartiles, range and IQR
5. 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
6. 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
7. Question WE8 · Siyavula Grade 10 Mathematics, 10.2 Measures of central tendency, Worked example 8 · 6 marks
WE8 The heights of $10$ learners are measured in centimetres to obtain the following data set:
${150; 172; 153; 156; 146; 157; 157; 143; 168; 157}$
Afterwards, we include one more learner in the group, who is exceptionally tall at $181 cm$ .
Compare the mean and median of the heights of the learners before and after the eleventh learner was included.(6)
Show the memo (6 ticks)Memo
1. ✓
  Mean of 10 learnersmean $= \frac{150 + 172 + 153 + 156 + 146 + 157 + 157 + 143 + 168 + 157}{10} = 155, 9 cm$
  1 mark · Calculate the mean
2. ✓
  Mean of 11 learnersmean $= \frac{150 + 172 + 153 + 156 + 146 + 157 + 157 + 143 + 168 + 157 + 181}{11} = 158, 2 cm$
  1 mark · Calculate the mean
3. ✓
  Median of 10 learnersSorted: ${143; 146; 150; 153; 156; 157; 157; 157; 168; 172}$
  median $= \frac{156 + 157}{2} = 156, 5 cm$
  1 mark · Find the median
4. ✓
  Median of 11 learnersSorted: ${143; 146; 150; 153; 156; 157; 157; 157; 168; 172; 181}$
  median $=$ sixth value $= 157 cm$
  1 mark · Find the median
5. ✓
  Compare the changesThe mean changes by $158, 2 - 155, 9 = 2, 3 cm$ when the outlier (the tall learner) is added, but the median changes by only $157 - 156, 5 = 0, 5 cm$ .
  1 mark · Interpret data and draw conclusions
6. ✓
  ConclusionIn general, the median is less affected by the addition of outliers to a data set than the mean is.
  1 mark · Interpret data and draw conclusions
8. 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
9. Question b · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 7 · 3 marks
In the previous worked example, the heights of $16$ adults were grouped into intervals of length $10 cm$ and drawn as the frequency polygon below.
Here is another data set of heights, this time of Grade $11$ learners.
$132; 132; 156; 147; 162; 168; 152; 174$
$141; 136; 161; 148; 140; 174; 174; 162$ $Diagram for this question$
b Compare the two frequency polygons on one graph to see the differences between the distributions.(3)
Show the memo (3 ticks)Memo
1. ✓
  Both polygons on one set of axesDraw the frequency polygons for the adults and for the Grade 11 learners on the same axes. $Memo diagram$
  1 mark · Draw a histogram, polygon or ogive
2. ✓
  Comparison: positionThe heights of the Grade $11$ learners are distributed more towards the left (shorter) than the heights of the adults.
  1 mark · Interpret data and draw conclusions
3. ✓
  Comparison: spreadThe learner heights also seem to be more evenly distributed between $130$ and $180 cm$ , whereas the adult heights are mostly between $160$ and $180 cm$ .
  1 mark · Interpret data and draw conclusions
10. 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

Measures of Dispersion Grade 10 videos

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

How to spot a misleading graph - Lea GaslowitzTED-Ed

Statistics Grade 10: QuartilesKevinmathscience

Modal Class Interval and Median class Interval for Grouped Continuous Data - Full Lesson and ExampleRadford Mathematics

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