INTERMEDIATE 2

1
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Graphs, Charts Tables
UNIT 2
Please choose a question to attempt from the
following
3
4
5
6
1
2
Stem Leaf
Dot Plot
Cum Freq Table
Dot to boxplot
Stem to boxplot
Piechart
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2
GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range

1. What is the probability that someone chosen at
   random earns less than 180?

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GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
Q1 is midpoint from start to median Q3 is
midpoint from median to end
Use median position (n1) / 2 to find median
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range
What would you like to do now?

1. What is the probability that someone chosen at
   random earns less than 180?

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GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
median 183
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range
Q1 171
What would you like to do now?
Q3 195
12

1. What is the probability that someone chosen at
   random earns less than 180?

2/5
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Question 1
1. Use median (n1) / 2 to find median
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
(a)(i) Since n 25 then the median is
13th value
ie median 183
(NOT 3!!!)
2. There are 12 values before median so Q1
position 13 - (12 1) / 2

• Median
• lower upper quartiles
• (iii) the semi-interquartile range

(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3
position 13 (12 1) / 2
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19th is 192 20th is 198 so Q3 195
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Question 1
4. Use SIQR ½ (Q3 Q1 ) / 2
(iii) SIQR ½(Q3 Q1)
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
(195 - 171) ? 2
12

• Median
• lower upper quartiles
• (iii) the semi-interquartile range

Begin Solution
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Question 1
5. Use P no of favourable / no of data
No of favourable ( under 180) 10
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
No of data n 25
(b) Prob(under 180) 10/25 2/5 .

• What is the probability that
• someone chosen at random
• earns less than 180?

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Comments
Median the middle number in the ordered list.
25 numbers in the list.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
1 12 13 14 - 25
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
12 numbers on either side of the median
median is the 13th number in order.
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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Comments
To find the upper and lower quartiles deal with
the numbers on either side of the median
separately.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
Q1
12 numbers before median. 6 numbers either side
of Q1 is midway between the
6th and 7th number.
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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Comments
To find the upper and lower quartiles deal with
the numbers on either side of the median
separately.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
Q3
12 numbers after median. 6 numbers either side of
Q3 is midway between the 19th
and 20th number.
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
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Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
Establish lowest highest values and draw line
with scale.
Plot a dot for each piece of data and label
diagram.
For probability use P no of favourable / no
of data
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Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
CLICK
Tightly clustered
3/10
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Question 2
1. Establish lowest highest values and draw
line with scale.

• 29 29 30 31
• 28 30 29 28
• 30 30 28 28
• 29 29 29 29 28

(a) Lowest 28 highest 31.
Illustrate this using a dot plot.
Begin Solution
2. Plot a dot for each piece of data and label
diagram.
Continue Solution
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Question 2
3. Make sure you know the possible descriptions
of data.

• 29 29 30 31
• 28 30 29 28
• 30 30 28 28
• 29 29 29 29 28

What type of distribution does this show?
Begin Solution
(b) Tightly clustered distribution.
Continue Solution
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Question 2
4. Use P no of favourable / no of data

• 29 29 30 31
• 28 30 29 28
• 30 30 28 28
• 29 29 29 29 28

Mode!
If a bag is chosen at random what is the
probability it will be heavier than the modal
weight?
Begin Solution
No of favourable ( bigger than 29) 6
Continue Solution
No of data n 20
Comments
(c) Prob(W gt mode) 6/20 3/10 .
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Comments
Other types of distribution
3. Make sure you know the possible descriptions
of data.
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(b) Tightly clustered distribution.
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Comments
Other types of distribution
3. Make sure you know the possible descriptions
of data.
Next Comment
(b) Tightly clustered distribution.
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Comments
Other types of distribution
3. Make sure you know the possible descriptions
of data.
Next Comment
(b) Tightly clustered distribution.
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20
Comments
To calculate simple probabilities
4. Use P no of favourable / no of data
Mode!
Probability
Number of favourable outcomes Number of
possible outcomes
No of favourable ( bigger than 29) 6
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No of data n 20
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(c) Prob(W gt mode) 6/20 3/10 .
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Charts, Graphs Tables Question 3
The results for a class test were 18
14 16 17 14 16 13 11 13 13 16 14 13
18 15 10 14 17 13 15 15 18 14 17 13
16 10 14 13 17 (a) Construct a cumulative
frequency table for this data. (b) What is the
median for this data? (c) What is the
probability that a pupil selected at random
scored under 14?
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Charts, Graphs Tables Question 3
The results for a class test were 18
14 16 17 14 16 13 11 13 13 16 14 13
18 15 10 14 17 13 15 15 18 14 17 13
16 10 14 13 17 (a) Construct a cumulative
frequency table for this data. (b) What is the
median for this data? (c) What is the
probability that a pupil selected at random
scored under 14?
Establish lowest highest values and draw
table.
Use median (n1) / 2 to establish in which row
median lies.
Complete each row 1 step at a time, calculating
running total as you go.
For probability use P no of favourable / no
of data
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Charts, Graphs Tables Question 3
The results for a class test were 18
14 16 17 14 16 13 11 13 13 16 14 13
18 15 10 14 17 13 15 15 18 14 17 13
16 10 14 13 17 (a) Construct a cumulative
frequency table for this data. (b) What is the
median for this data? (c) What is the
probability that a pupil selected at random
scored under 14?
CLICK
Median 14
1/3
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Question 3
1. Establish lowest highest values and draw a
table.

• 14 16 17 14 16 13 11 13
• 16 14 13 18 15 10 14 17
• 15 15 18 14 17 13 16 10
• 14 13 17

(a) Lowest 10 highest 18
10 11 12 13 14 15 16 17 18
2 2
1 3
0 3
7 10

• Construct a cumulative
• frequency table for this
• data.

6 16
3 19
4 23
4 27
Begin Solution
3 30
Continue Solution
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2. Complete each row 1 step at a time,
calculating running total as you go.
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Question 3
3. Use median (n1) / 2 to establish in which
row median lies.

• 14 16 17 14 16 13 11 13
• 16 14 13 18 15 10 14 17
• 15 15 18 14 17 13 16 10
• 14 13 17

10 11 12 13 14 15 16 17 18
2 2
1 3
0 3
7 10
6 16
(b) What is the median for this data?
3 19
4 23
4 27
What would you like to do now?
3 30
Begin Solution
Continue Solution
For 30 values median is between 15th 16th
both of which are in row 14.
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Median Mark 14
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Question 3
4. Use P no of favourable / no of data

• 14 16 17 14 16 13 11 13
• 16 14 13 18 15 10 14 17
• 15 15 18 14 17 13 16 10
• 14 13 17

10 11 12 13 14 15 16 17 18
2 2
1 3
0 3
7 10
6 16
(c) What is the probability that a pupil
selected at random scored under 14?
3 19
4 23
4 27
What would you like to do now?
3 30
Begin Solution
Continue Solution
No of favourable ( under 14) 10
Comments
No of data n 30
(c) Prob(marklt14) 10/30 1/3 .
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Comments
Median 1 15 Q2 16 - 30
10 11 12 13 14 15 16 17 18
2 2
1 3
0 3
7 10
6 16
Median 14
3 19
4 23
Find the mark at which the cumulative frequency
first reaches between 15th and 16th number.
4 27
3 30
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For 30 values median is between 15th 16th
both of which are in row 14.
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Median 14
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Comments
To calculate simple probabilities
Probability
10 11 12 13 14 15 16 17 18
2 2
1 3
Number of favourable outcomes Number of
possible outcomes
0 3
7 10
6 16
3 19
4 23
4 27
3 30
No of favourable ( under 14) 10
Next Comment
No of data n 30
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(c) Prob(marklt14) 10/30 1/3 .
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Charts, Graphs Tables Question 4
The dot plot below shows the number of matches
per box in a sample of 23 boxes.

1. Find the (i) median (ii) lower quartile
   (iii) upper quartile
2. Construct a boxplot using this data.
3. In a second sample the semi-interquartile range
   was 2.5. How does this distribution compare to
   the above sample?

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Charts, Graphs Tables Question 4
The dot plot below shows the number of matches
per box in a sample of 23 boxes.
Q1 is midpoint from start to median Q3 is
midpoint from median to end
Use median position (n1) / 2 to find median
remember bigger SIQR means more variation
(spread) in data.

1. Find the (i) median (ii) lower quartile
   (iii) upper quartile
2. Construct a boxplot using this data.
3. In a second sample the semi-interquartile range
   was 2.5. How does this distribution compare to
   the above sample?

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Charts, Graphs Tables Question 4
The dot plot below shows the number of matches
per box in a sample of 23 boxes.
Median 50
So Q1 49
So Q3 52

1. Find the (i) median (ii) lower quartile
   (iii) upper quartile
2. Construct a boxplot using this data.
3. In a second sample the semi-interquartile range
   was 2.5. How does this distribution compare to
   the above sample?

CLICK
the data is distributed more widely than (or not
as clustered as) the above data
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Question 4
1. Use median (n1) / 2 to find median

• (i) Sample size 23
• so median position is 12.
• ie (231)?2

Median 50
2. There are 11 values before median so Q1
position 12 - (11 1) / 2

• Find the (i) median
• (ii) lower quartile
• (iii) upper quartile

(ii) Middle of 1st 11 is position 6.
So Q1 49
3. There are 11 values after median so Q3
position 12 (11 1) / 2
Begin Solution
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(iii) Middle of 2nd 11 is position 18.
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So Q3 52
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Question 4
4. Draw number line with scale. Make sure you
note highest lowest as well as Q1, Q2, Q3.

• Lowest 48, Q1 49, Q2 50,
• Q3 52 Highest 58.

(b) Construct a boxplot using this data.
Begin Solution
Continue Solution
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Question 4
5. Calculate SIQR then compare remember bigger
SIQR means more variation (spread) in data.

• For above sample
• SIQR (52 - 49) ? 2 1.5

In a sample where the SIQR is 2.5 the data is
distributed more widely than (or not as clustered
as) the above data
(c) In a second sample the
semi-interquartile range was 2.5. How does
this compare?
What would you like to do now?
Begin Solution
Continue Solution
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Comments
The median
1. Use median (n1) / 2 to find median
23 numbers in the list

• (i) Sample size 23
• so median position is 12.
• ie (231)?2

1 - 11 12 13 - 23
Q2
Median 50
2. There are 11 values before median so Q1
position 12 - (11 1) / 2
11 numbers on either side of the median
(ii) Middle of 1st 11 is position 6.
So Q1 49
3. There are 11 values after median so Q3
position 12 (11 1) / 2
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(iii) Middle of 2nd 11 is position 18.
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So Q3 52
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Comments
For quartiles
1. Use median (n1) / 2 to find median

• (i) Sample size 23
• so median position is 12.
• ie (231)?2

1 - 5 6 7 - 11 12
Q2
Q1
Median 50
12
13 - 17 18 19 - 23
2. There are 11 values before median so Q1
position 12 - (11 1) / 2
Q3
Q2
(ii) Middle of 1st 11 is position 6.
Now count through the list until you reach the
6th, 12th,and 18th number in the list.
So Q1 49
3. There are 11 values after median so Q3
position 12 (11 1) / 2
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(iii) Middle of 2nd 11 is position 18.
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So Q3 52
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Comments
The semi-interquartile range is a measure of the
range of the middle 50.
5. Calculate SIQR then compare remember bigger
SIQR means more variation (spread) in data.

• For above sample
• SIQR (52 - 49) ? 2 1.5

It is a measure of how spread-out and so how
consistent or reliable the data is.
In a sample where the SIQR is 2.5 the data is
distributed more widely than or not as clustered
as the above data
Remember when asked to compare data always
consider average and spread.
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Charts, Graphs Tables Question 5
The stem leaf diagram below shows the weight
distribution of 26 people when they joined a
slimming club.
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Full solution
Comments

1. Find the median, lower upper quartiles for this
   data.
2. Use the data to construct a boxplot.
3. The boxplot below shows the weight distribution
   for these people after several months. Compare
   the two comment on the results.

EXIT
39
Charts, Graphs Tables Question 5
What now?
The stem leaf diagram below shows the weight
distribution of 26 people when they joined a
slimming club.
Q1 is midpoint from start to median Q3 is
midpoint from median to end
Use median position (n1) / 2 to find median
position
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When comparing two data sets comment on spread
and average
Reveal answer
Full solution
Comments

1. Find the median, lower upper quartiles for this
   data.
2. Use the data to construct a boxplot.
3. The boxplot below shows the weight distribution
   for these people after several months. Compare
   the two comment on the results.

EXIT
40
Charts, Graphs Tables Question 5
The stem leaf diagram below shows the weight
distribution of 26 people when they joined a
slimming club.
median 87
Menu
Q1 77
Q3 99
Full solution
Comments

1. Find the median, lower upper quartiles for this
   data.
2. Use the data to construct a boxplot.
3. The boxplot below shows the weight distribution
   for these people after several months. Compare
   the two comment on the results.

CLICK
CLICK
EXIT
41
Question 5
1. Use median (n1) / 2 to find median
(a)(i) Since n 26 then the median is
between 13th 14th value
ie median 87
2. There are 13 values before median so Q1
position is 6th value

• Find the median, lower
• upper quartiles for this data.

(ii) so Q1 77
3. There are 13 values after median so Q3
position is 20th position
Begin Solution
so Q3 99
Continue Solution
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Question 5
4. Draw number line with scale. Make sure you
note highest lowest as well as Q1, Q2, Q3.

• Lowest 60, Q1 77, Q2 87,
• Q3 99 Highest 123.

(b) Use the data to construct a boxplot.
Begin Solution
Continue Solution
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Question 5
5. Compare spread and relevant average.
(c) The boxplot below shows the weight
distribution for these people after several
months. Compare the two
comment on the results.

• Lightest has put on weight
• lowest now 65,
• heaviest 3 have lost weight
• highest now 115,
• median same but overall
• spread of weights has decreased
• as Q3-Q1 was 22
• but is now only 15.

Begin Solution
Continue Solution
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Comments
Remember To draw a boxplot you need a
five-figure summary
4. Draw number line with scale. Make sure you
note highest lowest as well as Q1, Q2, Q3.

• Lowest 60, Q1 77, Q2 87,
• Q3 99 Highest 123.

Box Plot
Lowest
Highest
Q1
Q2
Q3
five-figure summary
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Charts, Graphs Tables Question 6
The pie chart below shows the breakdown of how a
sample of 630 people spent their Saturday
nights.

• How many people
• went clubbing?
• (b) If 84 people went to the
• theatre then how big is x?

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46
Charts, Graphs Tables Question 6
The pie chart below shows the breakdown of how a
sample of 630 people spent their Saturday
nights.

• How many people
• went clubbing?
• (b) If 84 people went to the
• theatre then how big is x?

What would you like to do now?
Go to full solution
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47
Charts, Graphs Tables Question 6
The pie chart below shows the breakdown of how a
sample of 630 people spent their Saturday
nights.

• How many people
• went clubbing?
• (b) If 84 people went to the
• theatre then how big is x?

252
48
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48
Question 6
1. Set up ratio of angles and sectors and cross
multiply.
(a) The angle is 144 so ..
360 x amount 144 x 630
How many people went clubbing?
amount 144 x 630 ? 360
252
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Question 6
2. Set up ratio of angles and sectors and cross
multiply.
(b) The amount is 84 so ..
630 x angle 360 x 84
(b) If 84 people went to the theatre then
how big is x?
angle 360 x 84 ? 630
48
Begin Solution
Continue Solution
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Comments
Can also be tackled by using proportion
1. Set up ratio of angles and sectors and cross
multiply.
(a) The angle is 144 so ..
Amount x 630
360 x amount 144 x 630
amount 144 x 630 ? 360
252
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Comments
Can also be tackled by using proportion
2. Set up ratio of angles and sectors and cross
multiply.
(b) The amount is 84 so ..
630 x 84 x 360
630 x angle 360 x 84
angle 360 x 84 ? 630
End of graphs, charts etc.
48
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