basic_engineering_mathematics0

234 Basic Engineering Mathematics
a frequency distribution of about 8 classes for these
data.
39.8 40.1 40.3 40.0 40.6 39.7 40.0 40.4 39.6 39.3
39.6 40.7 40.2 39.9 40.3 40.2 40.4 39.9 39.8 40.0
40.2 40.1 40.3 39.7 39.9 40.5 39.9 40.5 40.0 39.9
40.1 40.8 40.0 40.0 40.1 40.2 40.1 40.0 40.2 39.9
39.7 39.8 40.4 39.7 39.9 39.5 40.1 40.1 39.9 40.2
39.5 40.6 40.0 40.1 39.8 39.7 39.5 40.2 39.9 40.3
2. Draw a histogram for the frequency distribution given in
the solution of Problem 1.
3. The information given below refers to the value of resistance
in ohms of a batch of 48 resistors of similar value.
Form a frequency distribution for the data, having about
6 classes and draw a frequency polygon and histogram
to represent these data diagramatically.
21.0 22.4 22.8 21.5 22.6 21.1 21.6 22.3
22.9 20.5 21.8 22.2 21.0 21.7 22.5 20.7
23.2 22.9 21.7 21.4 22.1 22.2 22.3 21.3
22.1 21.8 22.0 22.7 21.7 21.9 21.1 22.6
21.4 22.4 22.3 20.9 22.8 21.2 22.7 21.6
22.2 21.6 21.3 22.1 21.5 22.0 23.4 21.2
4. The time taken in hours to the failure of 50 specimens
of a metal subjected to fatigue failure tests are as shown.
Form a frequency distribution, having about 8 classes
and unequal class intervals, for these data.
28 22 23 20 12 24 37 28 21 25
21 14 30 23 27 13 23 7 26 19
24 22 26 3 21 24 28 40 27 24
20 25 23 26 47 21 29 26 22 33
27 9 13 35 20 16 20 25 18 22
5. Form a cumulative frequency distribution and hence
draw the ogive for the frequency distribution given in
the solution to Problem 3.
6. Draw a histogram for the frequency distribution given in
the solution to Problem 4.
7. The frequency distribution for a batch of 48 resistors of
similar value, measured in ohms, is:
20.5–20.9 3 21.0–21.4 10 21.5–21.9 11
22.0–22.4 13 22.5–22.9 9 23.0–23.4 2
Form a cumulative frequency distribution for these data.
8. Draw an ogive for the data given in the solution of
Problem 7.
9. The diameter in millimetres of a reel of wire is measured
in 48 places and the results are as shown.
2.10 2.29 2.32 2.21 2.14 2.22
2.28 2.18 2.17 2.20 2.23 2.13
2.26 2.10 2.21 2.17 2.28 2.15
2.16 2.25 2.23 2.11 2.27 2.34
2.24 2.05 2.29 2.18 2.24 2.16
2.15 2.22 2.14 2.27 2.09 2.21
2.11 2.17 2.22 2.19 2.12 2.20
2.23 2.07 2.13 2.26 2.16 2.12
(a) Form a frequency distribution of diameters having
about 6 classes.
(b) Draw a histogram depicting the data.
(c) Form a cumulative frequency distribution.
(d) Draw an ogive for the data.