Grade 10 Maths · Statistics

Find the median

Put the data in order and find the middle value (for example the median of 2, 5, 7, 9 is 6, the mean of 5 and 7).

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Grade 8 Data Handling: Mean, Median and ModeMaths Monkey

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Question 1.1 · November 2025 · Paper 2 · Provincial · 2 marks

The following data represent the prize allocation (in R1 000) for the top ten male finishers in the 2025 20 km Marathon, listed in descending order from 10th place to the first place. Note that the prize money for 6th place and 3rd place were not disclosed.

The mean prize across the available data is R21 770.

The prizes are shown in the table below. $Diagram for this question$

1.1 Calculate the value of

x

if the median

(Q_{2})

of the data is

9700

.(2)

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More past paper questions: find the median

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3. Question WE5 · Siyavula Grade 10 Mathematics, 10.2 Measures of central tendency, Worked example 5 · 2 marks
WE5 What is the median of ${11; 10; 14; 86; 2; 68; 99; 1}$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  Sort the values $1; 2; 10; 11; 14; 68; 86; 99$
  1 mark · Find the median
2. ✓
  MedianThere are $8$ values, an even number, so the median is halfway between the fourth and fifth values, $11$ and $14$ .
  Median $= \frac{11 + 14}{2} = 12, 5$
  1 mark · Find the median
4. Question WE4 · Siyavula Grade 10 Mathematics, 10.2 Measures of central tendency, Worked example 4 · 2 marks
WE4 What is the median of ${10; 14; 86; 2; 68; 99; 1}$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  Sort the values $1; 2; 10; 14; 68; 86; 99$
  1 mark · Find the median
2. ✓
  MedianThere are $7$ values, an odd number, so the median is the value in the fourth position.
  Median $= 14$
  1 mark · Find the median
5. Question WE1 · Siyavula Grade 11 Mathematics, 11.1 Revision, Worked example 1 · 3 marks
WE1 Compute the mean and median of the following data set:
$72, 5; 92, 6; 15, 6; 53, 0; 86, 4; 89, 9; 90, 9; 21, 7; 46, 0; 4, 1; 51, 7; 2, 2$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Mean $\overline{x} = \frac{626 , 6}{12} \approx 52, 22$
  1 mark · Calculate the mean
2. ✓
  Sort the values $2, 2; 4, 1; 15, 6; 21, 7; 46, 0; 51, 7; 53, 0; 72, 5; 86, 4; 89, 9; 90, 9; 92, 6$
  1 mark · Find the median
3. ✓
  MedianThere are an even number of values, so the median lies between the two middle values, $51, 7$ and $53, 0$ .
  Median $= \frac{51 , 7 + 53 , 0}{2} = 52, 35$
  1 mark · Find the median
6. 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

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