1.
|
a
|
b
|
c
|
d
|
e
|
|
|
(i)
|
12
|
17.20
|
6.6
|
62
|
824 000 mg
|
|
(ii)
|
5
|
12.48
|
4.2
|
48
|
9200 cg
|
|
(iii)
|
20
|
20.60
|
9.6
|
86
|
986 g
|
|
(iv)
|
15
|
8.12
|
5.4
|
38
|
894 g
|
|
(v)
|
41
|
17.45
|
6.2
|
54
|
1409 g
|
|
(vi)
|
14.01
|
15.8
|
6.63
|
65.5
|
697 g
|
|
(vii)
|
11.3
|
5.78
|
2.26
|
18.6
|
472 g
|
2. 10th percentile is 10, 90th percentile is 58.
.3. Find the mean of 12, 14, 17, 20, 21, 24 and complete the table below to help to find the standard deviation.
|
x
|
x −
 |
(x −
)2 |
|
12
|
12 − 18 = -6
|
36
|
|
14
|
14 − 18 = -4
|
16
|
|
17
|
17 − 18 = -1
|
1
|
|
20
|
20 − 18 = 2
|
4
|
|
21
|
21 − 18 = 3
|
9
|
|
24
|
24 − 18 = 6
|
36
|
|
Total Σ(x −
)2 = |
102
|
Standard deviation s = 4.12 (to 3 sig.fig.)
4. Find the mean and standard deviation of the following frequency distribution. Complete the table to assist your calculation.
|
x
|
f
|
x −
|
(x −
)2 |
f(x −
)2 |
|
1
|
4
|
1 − 2.72 = -1.72
|
2.9584
|
11.8336
|
|
2
|
6
|
2 − 2.72 = -0.72
|
0.5184
|
3.1104
|
|
3
|
9
|
3 − 2.72 = 0.28
|
0.0784
|
0.7056
|
|
4
|
5
|
4 − 2.72 = 1.28
|
1.6384
|
8.192
|
|
5
|
1
|
5 − 2.72 = 2.28
|
5.1984
|
5.1984
|
|
Σ
|
25
|
29.04
|
Standard deviation s = 1.08 (to 3 sig.fig.)
5. Standard deviation s = 5.03 (to 3 sig. fig.)
6. Standard deviation s = 1.19 (to 3 sig. fig.)
