PRESENTATION OF STATISTICAL DATA 537
J
- 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 poly-
gon 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
⎡
⎢
⎢
⎢
⎣
There is no unique solution,
but one solution 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
⎤
⎥
⎥
⎥
⎦
- The time taken in hours to the failure of 50
specimens of a metal subjected to fatigue fail-
ure tests are as shown. Form a frequency dis-
tribution, 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
242226 3212428402724
20 25 23 26 47 21 29 26 22 33
27 91335201620251822
⎡
⎢
⎣
There is no unique solution,
but one solution is: 1–10 3;
11–19 7; 20–22 12; 23–25 11;
26–28 10; 29–38 5; 39–48 2
⎤
⎥
⎦
- Form a cumulative frequency distribution and
hence draw the ogive for the frequency dis-
tribution given in the solution to Problem 3.
[
20. 95 3; 21.45 13; 21.95 24;
22 .45 37; 22.95 46; 23.45 48
]
- Draw a histogram for the frequency distribu-
tion given in the solution to Problem 4.
⎡ ⎢ ⎢ ⎢ ⎢ ⎣
Rectangles, touching one another,
having mid-points of 5.5, 15,
21, 24, 27, 33.5 and 43.5. The
heights of the rectangles (frequency
per unit class range) are 0.3,
0.78, 4. 4.67, 2.33, 0.5 and 0.2
⎤ ⎥ ⎥ ⎥ ⎥ ⎦
- The frequency distribution for a batch of
50 capacitors of similar value, measured in
microfarads, is:
[
10.5–10.9 2, 11.0–11.4 7,
11.5–11.9 10, 12.0–12.4 12,
12.5–12.9 11, 13.0–13.4 8
]
Form a cumulative frequency distribution for
these data.
[
(10.95 2), (11.45 9), (11.95 11),
(12.45 31), (12.95 42), (13.45 50)
]
- Draw an ogive for the data given in the
solution of Problem 7.
- 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 diame-
ters having about 6 classes.
(b) Draw a histogram depicting the data.
(c) Form a cumulative frequency distribu-
tion.
(d) Draw an ogive for the data.
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
(a) There is no unique solution,
but one solution is:
2.05–2.09 3; 2.10–21.4 10;
2.15–2.19 11; 2.20–2.24 13;
2.25–2.29 9; 2.30–2.34 2
(b) Rectangles, touching one
another, having mid-points of
2 .07, 2. 12 ...and heights of
3, 10,...
(c) Using the frequency
distribution given in the
solution to part (a) gives:
2 .095 3; 2.145 13; 2.195 24;
2 .245 37; 2.295 46; 2.345 48
(d) A graph of cumulative
frequency against upper
class boundary having
the coordinates given
in part (c).
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
