Download Topic 7 - Penang Free School

PENANG FREE SCHOOL
MATHEMATICS ELECTIVES- ADDITIONAL MATHEMATICS
DAVID CHNG YEANG SOON.
Try the following Questions. The answers are provided at the end of the questions.
Topic 7 Hard.
Name: ………………………………………..
Class:…………………..
1.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 14 and a standard deviation of 8.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 2 and then subtracted by 5,
find the
(i) new mean,
(ii) new variance.
[8 marks]
2.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 6 and a standard deviation of 8.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 3 and then subtracted by 3,
find the
(i) new mean,
(ii) new variance.
[8 marks]
3.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 9 and a standard deviation of 4.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 4 and then subtracted by 5,
find the
(i) new mean,
(ii) new variance.
[8 marks]
4.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 9 and a standard deviation of 6.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 4 and then subtracted by 3,
find the
(i) new mean,
(ii) new variance.
[8 marks]
5.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 11 and a standard deviation of 6.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 4 and then subtracted by 2,
find the
(i) new mean,
(ii) new variance.
[8 marks]
6.
25
26
27
28
29
Score
10
4
1
15
Number of participants 10
The table above shows the distribution of the scores obtained by 40 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
7.
10
11
12
13
14
Score
11
8
6
13
Number of participants 14
The table above shows the distribution of the scores obtained by 52 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
8.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 9 and a standard deviation of 7.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 2 and then subtracted by 8,
find the
(i) new mean,
(ii) new variance.
[8 marks]
9.
A set of number x1, x2, x3, x4, x5 and x6 has a mean of 10 and a standard deviation of 3.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 3 and then subtracted by 6,
find the
(i) new mean,
(ii) new variance.
10.
[8 marks]
15
16
17
18
19
Score
6
12
2
7
5
Number of participants
The table above shows the distribution of the scores obtained by 32 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
11. A set of number x1, x2, x3, x4, x5 and x6 has a mean of 15 and a standard deviation of 7.
(a) Find
(i) the sum of these six numbers,
(ii) the sum of the squares of these six numbers.
(b) If every number in the set of data is multiplied by 2 and then subtracted by 9,
find the
(i) new mean,
(ii) new variance.
[8 marks]
12.
29
30
31
32
33
Score
9
11
3
7
14
Number of participants
The table above shows the distribution of the scores obtained by 44 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
13.
23
24
25
26
27
Score
7
6
4
7
Number of participants 12
The table above shows the distribution of the scores obtained by 36 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
14.
Score
Number of participants
25
3
26
5
27
5
28
12
29
7
The table above shows the distribution of the scores obtained by 32 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
15.
23
24
25
26
27
Score
1
9
11
10
13
Number of participants
The table above shows the distribution of the scores obtained by 44 participants in a
competition. Find
(a) the range,
(b) the interquartile range,
(c) the mean,
(d) the variance,
(e) the standard deviation
of the distribution.
[8 marks]
Answers:
1. (a) (i) 84
(ii) 1560
(b) (i) 23
(ii) 256
2. (a) (i) 36
(ii) 600
(b) (i) 15
(ii) 576
3. (a) (i) 54
(ii) 582
(b) (i) 31
(ii) 256
4. (a) (i) 54
(ii) 702
(b) (i) 33
(ii) 576
5. (a) (i) 66
(ii) 942
(b) (i) 42
(ii) 576
6. (a) Range = 4
(b) Interquartile range = 4
(c) Mean = 27.025
(d) 2 = 2.774
7.
8.
9.
10.
11.
12.
13.
14.
15.
(e)  = 1.666
(a) Range = 4
(b) Interquartile range = 3
(c) Mean = 11.865
(d) 2 = 2.386
(e)  = 1.545
(a) (i) 54
(ii) 780
(b) (i) 10
(ii) 196
(a) (i) 60
(ii) 654
(b) (i) 24
(ii) 81
(a) Range = 4
(b) Interquartile range = 2
(c) Mean = 16.781
(d) 2 = 1.921
(e)  = 1.386
(a) (i) 90
(ii) 1644
(b) (i) 21
(ii) 196
(a) Range = 4
(b) Interquartile range = 3
(c) Mean = 31.136
(d) 2 = 2.481
(e)  = 1.575
(a) Range = 4
(b) Interquartile range = 3
(c) Mean = 24.639
(d) 2 = 2.286
(e)  = 1.512
(a) Range = 4
(b) Interquartile range = 2
(c) Mean = 27.469
(d) 2 = 1.562
(e)  = 1.25
(a) Range = 4
(b) Interquartile range = 2
(c) Mean = 25.568
(d) 2 = 1.382
(e)  = 1.175