Grade 10 Maths · Statistics · Paper 2

Representation of Data Grade 10

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

past paper questions: 19 past paper questions
skills: 3 skills
videos: 3 videos

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Question 4.5 · September 2024 · Provincial · 3 marks

At a School Athletics Day, a stopwatch was used to find the time it took a group of athletes to run the 200m event. The results were recorded in a frequency table. Diagram for this question

4.5 Represent the data on a histogram, using the attached DIAGRAM SHEET.(3) Diagram for question 4.5

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More Representation of Data Grade 10 questions and answers

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4. Question WE9 · Siyavula Grade 10 Mathematics, 10.3 Grouping data, Worked example 9 · 3 marks
$Diagram for this question$
WE9 The heights in centimetres of $30$ learners are given below.

Group the data into the following ranges and draw a histogram of the grouped data:
$130 \leq h < 140$
$140 \leq h < 150$
$150 \leq h < 160$
$160 \leq h < 170$
$170 \leq h < 180$
(Note that the ranges do not overlap since each one starts where the previous one ended.)(3)
Show the memo (3 ticks)Memo
1. ✓
  Count the values in each range $130 \leq h < 140$ : $7$
  $140 \leq h < 150$ : $5$
  $150 \leq h < 160$ : $7$
  $160 \leq h < 170$ : $9$
  $170 \leq h < 180$ : $2$
  1 mark · Read and complete a frequency table
2. ✓
  Bars on the rangesThere are $5$ ranges, so the histogram has $5$ rectangles. The base of each rectangle is its range on the height axis: $130$ to $140$ , $140$ to $150$ , and so on, with no gaps between them.
  1 mark · Draw a histogram, polygon or ogive
3. ✓
  Heights of the barsThe height of each rectangle is the count in its range: $7$ , $5$ , $7$ , $9$ and $2$ (see the histogram). $Memo diagram$
  1 mark · Draw a histogram, polygon or ogive
5. Question WE5 · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 5 · 4 marks
WE5 The following data represent the heights of $16$ adults in centimetres.
$162; 168; 177; 147; 189; 171; 173; 168$
$178; 184; 165; 173; 179; 166; 168; 165$
Divide the data into $5$ equal length intervals between $140 cm$ and $190 cm$ and draw a histogram.(4)
Show the memo (4 ticks)Memo
1. ✓
  IntervalsTo have $5$ intervals of the same length between $140$ and $190$ , we need an interval length of $10$ .
  The intervals are $(140; 150]$ ; $(150; 160]$ ; $(160; 170]$ ; $(170; 180]$ and $(180; 190]$ .
  1 mark · Read and complete a frequency table
2. ✓
  Counts $(140; 150]$ : $1$ ; $(150; 160]$ : $0$ ; $(160; 170]$ : $7$ ; $(170; 180]$ : $6$ ; $(180; 190]$ : $2$
  1 mark · Read and complete a frequency table
3. ✓
  Bars on the intervalsDraw one rectangle on each interval of the height axis, from $140$ to $190$ , with no gaps between the intervals.
  1 mark · Draw a histogram, polygon or ogive
4. ✓
  Heights of the barsThe heights of the rectangles are the counts: $1$ , $0$ , $7$ , $6$ and $2$ (see the histogram). $Memo diagram$
  1 mark · Draw a histogram, polygon or ogive
6. Question WE6 · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 6 · 2 marks
$Diagram for this question$
WE6 The histogram below shows the heights of $16$ adults in centimetres (from the previous worked example). Use the histogram to draw a frequency polygon of the same data.(2)
Show the memo (2 ticks)Memo
1. ✓
  Points at the midpointsMark the middle of the top of each rectangle: the points $(145; 1)$ , $(155; 0)$ , $(165; 7)$ , $(175; 6)$ and $(185; 2)$ .
  1 mark · Draw a histogram, polygon or ogive
2. ✓
  Join the pointsDraw line segments between the points and remove the histogram to show only the frequency polygon. $Memo diagram$
  1 mark · Draw a histogram, polygon or ogive
7. Question a · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 7 · 2 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.
$132; 132; 156; 147; 162; 168; 152; 174$
$141; 136; 161; 148; 140; 174; 174; 162$ $Diagram for this question$
a Draw the frequency polygon for this data set using the same interval length as in the previous example.(2)
Show the memo (2 ticks)Memo
1. ✓
  Frequency table $(130; 140]$ : $4$ ; $(140; 150]$ : $3$ ; $(150; 160]$ : $2$ ; $(160; 170]$ : $4$ ; $(170; 180]$ : $3$
  1 mark · Read and complete a frequency table
2. ✓
  Frequency polygonPlot the counts above the midpoints of the intervals, $(135; 4)$ , $(145; 3)$ , $(155; 2)$ , $(165; 4)$ and $(175; 3)$ , and join them with line segments. $Memo diagram$
  1 mark · Draw a histogram, polygon or ogive
8. Question WE4 · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 4 · 5 marks
$Diagram for this question$
WE4 Use the following histogram to determine the events that were recorded and the relative frequency of each event. Summarise your answer in a table.(5)
Show the memo (5 ticks)Memo
1. ✓
  Events and countsThe events are shown on the $x$ -axis: not yet in school, in primary school and in high school.
  The height of each rectangle gives the count: not yet in school: $2$ ; in primary school: $5$ ; in high school: $9$ .
  1 mark · Use bar, pie and line graphs
2. ✓
  Total frequency $2 + 5 + 9 = 16$
  1 mark · Read and complete a frequency table
3. ✓
  Relative frequency: not yet in school $\frac{2}{16} = \frac{1}{8}$
  1 mark · Use relative frequency
4. ✓
  Relative frequency: in primary school $\frac{5}{16}$
  1 mark · Use relative frequency
5. ✓
  Relative frequency: in high school $\frac{9}{16}$
  Summary: not yet in school: count $2$ , relative frequency $\frac{1}{8}$ ; in primary school: count $5$ , relative frequency $\frac{5}{16}$ ; in high school: count $9$ , relative frequency $\frac{9}{16}$ .
  1 mark · Use relative frequency
9. Question d · Siyavula Grade 8 Mathematics, 19 Represent data, Bar graphs, Worked example 19.1 · 2 marks
The school tuckshop staff kept a record of how many hot dogs, sandwiches, salads and burgers they sold in one day. The bar graph represents the data they collected. $Diagram for this question$
d How many more sandwiches than salads did they sell?(2)
Show the memo (2 ticks)Memo
1. ✓
  Read both valuesReading the values off the vertical axis: $35$ sandwiches and $10$ salads were sold.
  1 mark · Use bar, pie and line graphs
2. ✓
  Difference $35 - 10 = 25$ , so there were $25$ more sandwiches sold than salads.
  1 mark · Use bar, pie and line graphs
10. Question WE19.2 · Siyavula Grade 8 Mathematics, 19 Represent data, Bar graphs, Worked example 19.2 · 3 marks
$Diagram for this question$
WE19.2 A spaza shop collected data about how many customers visited every month. Draw a bar graph for the data given in the table.(3)
Show the memo (3 ticks)Memo
1. ✓
  Categories on the horizontal axisUse the five months, January to May, as the categories on the horizontal axis.
  1 mark · Use bar, pie and line graphs
2. ✓
  Scale on the vertical axisThe lowest value is $100$ and the highest is $500$ , so use a scale from $0$ to $600$ with intervals of $100$ for the number of customers.
  1 mark · Use bar, pie and line graphs
3. ✓
  Draw the barsDraw each bar to the correct height using the data in the table. Label the categories, the scale and the axes, and give the graph a heading such as 'Number of customers per month' (see the graph). $Memo diagram$
  1 mark · Use bar, pie and line graphs

Representation of Data Grade 10 videos

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

Grade 8 Data Handling: Tally tables and frequency tablesMaths Monkey

How To Make a Histogram Using a Frequency Distribution TableThe Organic Chemistry Tutor

Bar Charts and Bar Graphs ExplainedMashup Math

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