Grade 10 Maths · Statistics · Work back from a mean or spread

Work back from a mean or spread Grade 10

Use a given mean, median, interquartile range or standard deviation to find a missing or unknown data value, and say how the statistics change when a constant is added to every value.

questions use it, all grades · 10 past paper, 24 practice: 34 questions use it, all grades · 10 past paper, 24 practice
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How to find the missing value when given the meanCowan Academy

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Adding Vs. Multiplying Effect on Median and Standard DeviationMario's Math Tutoring

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Question 2.2 · November 2025 · Paper 2 · National (DBE) · 5 marks

There are 9 players in a basketball team. The coach calculated that on average, each player scored 12 points during a game. The points scored by 8 of the 9 players from the team is given below: $Diagram$

2.2 How many players' points score was outside ONE standard deviation of the mean points score?(5)

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

More past paper questions: work back from a mean or spread

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3. Question 1.2.1 · November 2017 · Paper 2 · National (DBE) · 2 marks
1.2 A group of 13 students indicated how long it took (in hours) before their cellphone batteries required recharging. The information is given in the table below.

Answer the questions that follow. $Diagram for question 1.2$
1.2.1 Calculate the value of $y$ if the mean for this data set is $41$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Mean equationMean $= \frac{439 + y}{13}$
  $41 = \frac{439 + y}{13}$
  1 mark · Work back from a mean or spread
2. ✓
  Answer $439 + y = 533$
  $y = 94$
  1 mark · Calculate the mean
4. Question 2.4 · November 2023 · Paper 2 · National (DBE) · 4 marks
At a certain school, the staff committee wanted to determine how many glasses of water the staff members drank during a school day. All teachers present on a specific day were interviewed. The information is shown in the table below. $Diagram for this question$
2.4 The staff committee observed that $k$ teachers were absent on the day of the interviews. It was found that half of these $k$ teachers drank from 0 to fewer than 2 (that is $0 \leq x < 2$ ) glasses of water per day, while the remainder of them drank from 4 to fewer than 6 (that is $4 \leq x < 6$ ) glasses of water per day. When these $k$ teachers are included in the data, the estimated mean is 4 glasses of water per staff member per day.

How many teachers were absent on the day of the interviews?(4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: Answer from Q2.2 + $k$ $\overset{x}{ˉ} = \frac{1 ( 5 + \frac{k}{2} ) + 3 ( 15 ) + 5 ( 13 + \frac{k}{2} ) + 7 ( 5 ) + 9 ( 2 )}{40 + k} = 4$
  1 mark · Estimate the mean of grouped data
2. ✓
  METHOD 1: $1 (5 + \frac{k}{2})$ $1 \times (5 + \frac{k}{2})$
  1 mark · Estimate the mean of grouped data
3. ✓
  METHOD 1: $5 (13 + \frac{k}{2})$ $5 \times (13 + \frac{k}{2})$
  1 mark · Estimate the mean of grouped data
4. ✓
  METHOD 1: Answer $5 + \frac{k}{2} + 45 + 65 + \frac{5 k}{2} + 35 + 18 = 160 + 4 k$
  $3 k + 168 = 160 + 4 k$
  $k = 8$
  1 mark · Work back from a mean or spread
5. Question 1.5 · November 2018 · Paper 2 · National (DBE) · 3 marks
A school held a sports day. One of the items on the programme was an obstacle race. Teams of 10 parents and learners participated in this race. The table below shows the time taken, in minutes, by each member of a particular team to complete the race. $Diagram for this question$
1.5 It took another team a total time of $x + 5$ minutes to complete the race. Calculate the value of $x$ if the overall mean of the two teams combined was 18 minutes.(3)
Show the memo (3 ticks)Memo
1. ✓
  Total of both teams: $169 + x + 5$ Total time of both teams $= 169 + x + 5$
  1 mark · Calculate the mean
2. ✓
  Dividing by 20 $\frac{169 + x + 5}{20} = 18$
  1 mark · Work back from a mean or spread
3. ✓
  Answer $x = 18 \times 20 - 174$
  $x = 186$
  1 mark · Calculate the mean
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 · Work back from a mean or spread
3. ✓
  New mean equationNew $\overset{x}{ˉ}$ : $\frac{247 + x}{16} = 16$
  1 mark · Work back from a mean or spread
4. ✓
  Value of $x$ $∴ x = 9$
  1 mark · Calculate the mean

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