Grade 10 Maths · Statistics · Find quartiles, range and IQR

Quartiles and Interquartile Range Grade 10

Find the quartiles, range and interquartile range of ordered data, for example in 2, 4, 6, 8, 10, 12, 14 the IQR is 12 − 4 = 8.

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Statistics Grade 10: QuartilesKevinmathscience

Quartiles | Lower Quartile, Median, and Upper Quartile | Math with Mr. JMath with Mr. J

Interquartile Range (IQR) | Math with Mr. JMath with Mr. J

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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.

More past paper questions: find quartiles, range and iqr

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3. 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
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 1.4.3 · 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

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