Download Tutorial 8 - UniMAP Portal

UNIVERSITI MALAYSIA PERLIS
INSTITUT MATEMATIK KEJURUTERAAN
TUTORIAL 8
Statistics
1. A sample of 8 companies in the motorbicycle industry was surveyed as to their return on
investment last year. The results are (in percent): 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2 and
15.6. Calculate the
i) mean
ii) median
iii) mode
2. Ten experts rated a newly developed pizza on a scale of 1 to 5. The ratings were: 34, 35, 41, 28,
26, 29, 32, 36, 38, and 40. Find the
i) range
ii) mean
iii) standard deviation
3. The thickness of 40 samples of steel plate were measured:
Thickness
9.60-9.80 9.90-10.1 10.2-10.4 10.5-10.7 10.8-11.0 11.1-11.3 11.4-11.6
x (mm)
Frequency
1
4
10
11
7
4
3
f
Using coding procedure, calculate:
i)
the mean
ii)
the standard deviation
iii)
the mode
iv)
the median of the set of values given
4. The lengths of 50 copper plugs gave the following frequency distribution:
Length
14.0-14.2 14.3-14.5 14.6-14.8 14.9-15.1 15.2-15.4 15.5-15.7 15.8-1.0
x (mm)
Frequency
2
4
9
15
11
6
3
f
i)
ii)
calculate the mean and standard deviation
for a full batch of 2400 plugs, calculate (a) the limits between which all the lengths are
likely to occur, (b) the number of plugs with lengths greater than 15.09 mm.
5. The number of components processed in one hour on a new machine was recorded on 40
occasions:
66
80
76
77
i)
ii)
87
71
83
67
79
91
75
76
74
62
71
82
84
77
83
78
72
86
67
88
81
87
94
66
78
72
64
79
68
80
82
74
74
77
78
64
divide the set of values into seven equal width classes from 60 to 94.
Calculate (a) the frequency distribution (table), (b) the mean, (c) the standard deviation.
6. A machine is set to produce bolts of nominal diameter 25.0 mm. Measurement of the diameters
of 60 bolts gave the following frequency distribution:
Diameter
23.3-23.7 23.8-24.2 24.3-24.7 24.8-25.2 25.3-25.7 25.8-26.2 26.3-26.7
x (mm)
Frequency
2
4
10
17
16
8
3
f
i)
ii)
calculate (a) the mean diameter and (b) the standard deviation from the mean.
For a full run of 3000, calculate (a) the limits between which all the diameters are likely
to lie, (b) the number of bolts with diameters less than 24.45 mm.
SOLUTION
TUTORIAL 8
1. i)
13.85 ii)
27.4
iii)
14.8
2. i)
15
33.9
iii)
s=5.11
ii)
3. i ) x  10.62 mm ii )   0.437 mm iii ) mod e  10.51 mm iv ) median  10.59mm
4. i)
5. i)
x  15.05mm   0.4314mm ii ) a) 13.76  16.34mm b) 1200
ii)
a)
x
60-64
65-69
70-74
75-79
80-84
85-89
90-94
ii)
6. i)
f
3
5
7
11
8
4
2
n   f  40
b) x  76.5
a) x  25.14mm
c)   7.73
b)   0.690mm
ii)
a) 23.07 - 27.21mm
b) 480