MATHEMATICS
MORE EXERCISES
Statistics.

Question  1
Listed below are the marks of 40 pupils :

23; 6; 12; 18; 24; 6; 9; 14; 21; 11
9; 17; 11; 16; 13; 19; 15; 11; 8; 16
13; 12; 7; 14; 9; 17; 8; 12; 21; 12
17; 13; 14; 6; 13; 19; 18; 13; 9; 11

1.1  Complete the table below :

 Klas middelpunt (x) Class midpoint Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. f . x 0 < p ≤ 5 5 < p ≤ 10 10 < p ≤ 15 15 < p ≤ 20 20 < p ≤ 25
[ A 1.1 ]

1.2  Determine the mean of the
grouped data.                                              [ A 1.2 ]

1.3  Which interval is the modal
interval?                                                       [ A 1.3 ]

1.4  In which interval does the following lie?
1.4.1  Q1                                                              [ A 1.4.1 ]
1.4.2  Q2                                                              [ A 1.4.2 ]
1.4.3  Q3                                                              [ A 1.4.3 ]
1.4.4  the 90th  percentile                                [ A 1.4.4 ]

1.5  Draw a neat ogive of the data.                [ A 1.5 ]

1.6.1  Use the ogive to determine the
values of the quartiles.                         [ A 1.6.1 ]
1.6.2  Determine the inter quartile
range (IQR).                                             [ A 1.6.2 ]
1.7  Write down the five number
summary of the data.                               [ A 1.7 ]
1.8  Draw a neat box and whisker
diagram to represent the data.               [ A 1.8 ]
1.9  Is the data skewed? Give a reason.        [ A 1.9 ]
1.10  What is the lowest mark for the
top 10% of the pupils?                            [ A 1.10 ]

Question  2
Listed below is the mass of each of 20 boys :

72;   51;   48;   66;   57;   77;   83;   65;   53
75;   67;   64;   47;   58;   74;   62;   81;   65
69;   73

2.1  Complete the table below :

 Klas middelpunt (x) Class midpoint Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. f . x 40 < m ≤ 50 50 < m ≤ 60 60 < m ≤ 70 70 < m ≤ 80 80 < m ≤ 90

[ A 2.1 ]

2.2  Determine the mean of the
grouped data.                                              [ A 2.2 ]

2.3  Which interval is the modal
interval?                                                       [ A 2.3 ]

2.4  In which interval does the following lie?
2.4.1  Q1                                                              [ A 2.4.1 ]
2.4.2  Q2                                                              [ A 2.4.2 ]
2.4.3  Q3                                                              [ A 2.4.3 ]
2.4.4  the 30th  percentile                                [ A 2.4.4 ]
2.4.5  the 8th  decile                                          [ A 2.4.5 ]

2.5  Draw a neat ogive of the data.                [ A 2.5 ]

2.6.1  Use the ogive to determine the
values of the quartiles.                         [ A 2.6.1 ]
2.6.2  Determine the inter quartile
range (IQR).                                             [ A 2.6.2 ]
2.7  Write down the five number
summary of the data.                               [ A 2.7 ]
2.8  Draw a neat box and whisker
diagram to represent the data.               [ A 2.8 ]
2.9  Is the data skewed? Give a reason.        [ A 2.9 ]

Question  3
The frequency table below summarises
the height of 40 pupils :

 Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. Klas middelpunt (x) Class midpoint f . x 140 < h ≤ 150 3 150 < h ≤ 160 10 160 < h ≤ 170 14 170 < h ≤ 180 12 180 < h ≤ 190 1

3.1  Complete the table above.                       [ A 3.1 ]
3.2  Determine the mean of the
grouped data.                                             [ A 3.2 ]

3.3  Draw an ogive for the data.                     [ A 3.3 ]

3.4  Show on the ogive the position of
each quartile.                                              [ A 3.4 ]

3.5  Determine the inter quartile
range (IQR)                                                  [ A 3.5 ]

3.6  What is the minimum height of the
taller 50% of the pupils?                          [ A 3.6 ]

Question  4
The frequency table below summarises the time
that 20 workmen need to complete a certain task :

 Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. Klas middelpunt (x) Class midpoint f . x 5 < t ≤ 10 4 10 < t ≤ 15 8 15 < t ≤ 20 6 20 < t ≤ 25 2

4.1  Complete the table above.                       [ A 4.1 ]
4.2  Determine the mean of the
grouped data.                                               [ A 4.2 ]

4.3  Determine the modal interval.               [ A 4.3 ]

4.4  Draw an ogive for the data.                     [ A 4.4 ]

4.5  Show on the ogive the position of
Q1 and Q3.                                                   [ A 4.5 ]

4.6  Determine the inter quartile range
(IQR).                                                            [ A 4.6 ]

4.7  What is the longest time needed by
the fastest 25% of the workers to finish
the task?                                                      [ A 4.7 ]

Question  5
The frequency table below summarises the age
of 60 shoppers :

 Frequency f Cum. Frekq. cf Class midpoint (x) f . x 10 < a ≤ 20 5 20 < a ≤ 30 19 30 < a ≤ 40 25 40 < a ≤ 50 11

5.1  Complete the table above.                       [ A 5.1 ]
5.2  Determine the mean of the
grouped data.                                             [ A 5.2 ]

5.3  Draw an ogive for the data.                    [ A 5.3 ]

5.4  Show on the ogive the position of
5.4.1  Q1                                                              [ A 5.4.1 ]
5.4.2  Q3                                                              [ A 5.4.2 ]
5.4.3  4th  decile.                                               [ A 5.4.3 ]

5.5  Determine the inter quartile range
(IQR).                                                            [ A 5.5 ]

5.6  What is the youngest age of the 60% of
the eldest shoppers?                                 [ A 5.6 ]

Question  6
The accompanying frequency table
summarises the marks of 40 pupils for
a test with a maximum mark if 25 :

6.1  Use the data presented by the ogive to
complete the frequency table below :

 Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. Klas middelpunt (x) Class midpoint f . x 0 < p ≤ 5 5 < p ≤ 10 10 < p ≤ 15 15 < p ≤ 20 20 < p ≤ 25
[ A 6.1 ]

6.2  Determine the mean of the
grouped data.                                             [ A 6.2 ]

6.3  How many pupils obtained less
than 10 marks?                                          [ A 6.3 ]

6.4  What percentage of the pupils
passed if the pass mark is 40%?             [ A 6.4 ]

6.5  How many pupils obtained 80%
or more?                                                      [ A 6.5 ]

6.6  What is the highest possible mark
for the bottom 50% of the pupils?          [ A 6.6 ]

6.7  What is the lowest mark for the
top 25% of the pupils?                              [ A 6.7 ]

Question  7
The ogive represents the mass, in kg,
of 60 pupils :

7.1  Use the data presented by the ogive to
complete the frequency table below :

 Frekwensie f Frequency Kum. Frekw. cf Cum. Freq. Klas middelpunt (x) Class midpoint f . x 40 < m ≤ 50 50 < m ≤ 60 10 < m ≤ 15 60 < m ≤ 70 70 < m ≤ 80 80 < m ≤ 90

[ A 7.1 ]

7.2  Determine the mean of the
grouped data.                                             [ A 7.2 ]

7.3  What is the greatest mass of the lightest
25% of the pupils?                                     [ A 7.3 ]

7.4  How many pupils have a mass
greater than 65 kg?                                   [ A 7.4 ]

7.5  What percentage of the pupils have
a mass between 70 kg and 80 kg,
i.e. 70 < m ≤ 80?                                        [ A 7.5 ]

Question  8
The box and whisker diagram below
summarises the monthly salaries of
27 employees of a firm.
No two employees earn the same salary.

8.1  How many employees earn less
than R7 000?                                               [ A 8.1 ]

8.2  What is the smallest salary and what
is the highest salary earned by the
top 50% of the employees?                      [ A 8.2 ]

8.3  Determine whether there are
any outliers.                                                [ A 8.3 ]

Question  9
Study the box and whisker diagram below

9.1  Is the data skewed? Explain.                   [ A 9.1 ]

9.2  Are there any outliers? Do the necessary

Question  10
Study the box and whisker diagram below

10.1  Is the data skewed? Explain.                 [ A 10.1 ]

10.2  Are there any outliers? Do the necessary

Question  11
The number of hours worked overtime
by employees are as follows :

42;   22;   50;   66;   35;   36;   76;   29;   33;   52;   43

11.  Determine the following :
11.1.1  the mean.                                             [ A 11.1.1 ]
11.1.2  the three quartiles.                            [ A 11.1.2 ]
11.1.3  the interquartile range, IQR.           [ A 11.1.3 ]

11.2  Is the data skewed? Explain.               [ A 11.2 ]
11.3  Are there any outliers? Do the
necessary calcultions to prove

Question  12
The age, in years, of 20 people are as follows :

20;   40;   43;   17;   38;   52;   61;   16;   14;   25;
38;   35;   84;   72;   53;   22;   32;   33;   24;   48

12.1  Determine the following :
12.1.1  the mean.                                           [ A 12.1.1 ]
12.1.2  the standard deviation.                   [ A 12.1.2 ]
12.2  How many people's age lie outside
one standard deviation of the mean?
[ A 12.2 ]

Question  13
The weekly abscence of a Grade 11 class
during the second quarter is shown below.

33;   20;   18;   15;   30;   26;   19;   15;   10;   24

13.1  Determine the following :
13.1.1  the mean.                                           [ A 13.1.1 ]
13.1.2  the standard deviation.                   [ A 13.1.2 ]
13.2  Find the number of weeks that
the weekly abscence was inside
one standard deviation of the mean.
[ A 13.2 ]

Question  14
The time, in minutes, taken by 10 runners
to complete a race is given below :

33;   20;   18;   15;   30;   26;   19;   15;   10;   24

14.1  Determine the following :
14.1.1  the mean.                                           [ A 14.1.1 ]
14.1.2  the standard deviation.                   [ A 14.1.2 ]
14.2  How many runners completed the
race within one standard deviation
of the mean?                                             [ A 14.2 ]